IE 360 PROJECT

GROUP 21

Hayrettin İlbey GÜNGÖR 2018402183

Hamza KALE 2018402204

Hasan Alp YILDIZLAR 2018402201

Required Packages

install.packages('readxl')
install.packages('RcppRoll')
install.packages('data.table')
install.packages('ggplot2')
install.packages('lubridate')
install.packages('scales')
install.packages('forecast')
install.packages('GGally')
install.packages('dplyr')
install.packages('corrplot')
install.packages('ggcorrplot')
install.packages('zoo')
install.packages('M3')
install.packages('ggplot2')
install.packages('urca')

Installing readxl [1.4.0] ...
	OK [linked cache]
Installing RcppRoll [0.3.0] ...
	OK [linked cache]
Installing data.table [1.14.2] ...
	OK [linked cache]
Installing ggplot2 [3.3.6] ...
	OK [linked cache]
Installing lubridate [1.8.0] ...
	OK [linked cache]
Installing scales [1.2.0] ...
	OK [linked cache]
Installing forecast [8.16] ...
	OK [linked cache]
Installing GGally [2.1.2] ...
	OK [linked cache]
Installing dplyr [1.0.9] ...
	OK [linked cache]
Installing corrplot [0.92] ...
	OK [linked cache]
Installing ggcorrplot [0.1.3] ...
	OK [linked cache]
Installing zoo [1.8-10] ...
	OK [linked cache]
Installing M3 [0.3] ...
	OK [linked cache]
Installing ggplot2 [3.3.6] ...
	OK [linked cache]
Installing urca [1.3-0] ...
	OK [linked cache]

library(readxl)
library(ggplot2)
library(RcppRoll)
library(data.table)
library(ggplot2)
library(lubridate)
library(scales)
library(forecast)
library(GGally)
library(dplyr)
library(corrplot)
library(ggcorrplot)
library(zoo)
library(M3)
library(urca)

Introduction

Problem Description

To create a sustainable world, it is vital to use sustainable energy sources such as solar energy. In order to use solar energy with maximum benefit, it is necessary to evaluate different alternatives. In this project, the solar power plant named KIVANC 2 GES located in Mersin (between 36-37° north latitude and 33-35° east longitude) is inspected. In this study, the average daily amount of energy produced will be compared and the location where energy can be produced with maximum efficiency will be determined via forecasts.

Descriptive Analysis of the Given Data

The raw data were obtained from KIVANC 2 GES. The first of these data includes 4 different metrics (TEMP, REL_HUMIDITY, DSWRF, CLOUD_LOW_LAYER; will be explained in detail in the 2nd part) for 9 different locations, and includes hour-based information between 2/1/2021 and 6/6/2022. In addition, as a second data, the daily energy production amount between these dates was from KIVANC 2 GES. When the data is analyzed in general, one of the striking situations is that between 8.00 pm and 04.00 am, the energy production sees approximately 0 value and peak value between 10.00 am and 04.00 pm. This situation shows us that there is a daily seasonality. While it is quite normal to produce more energy during periods of increased sun exposure, it is quite normal for it not to produce energy when the sun is not present. In addition, it is seen that 4 different metrics affect the production amount in different ways. For example, it is seen that the negative effect of cloud amount on energy production is more than the effect of temperature factor on energy production.

Summary of the Proposed Approach

PART 3 ÖZET R kullandık, .. methodları kullandık lag variable olarak şunu kullandık

Data Manipulation

Data <- read.csv('data/2022-05-30_weather.csv')

wide_data <- dcast(Data, date + hour ~ variable + lat + lon, value.var = "value")

Warning message in dcast(Data, date + hour ~ variable + lat + lon, value.var = "value"):
“The dcast generic in data.table has been passed a data.frame and will attempt to redirect to the reshape2::dcast; please note that reshape2 is deprecated, and this redirection is now deprecated as well. Please do this redirection yourself like reshape2::dcast(Data). In the next version, this warning will become an error.”

wide_data <- data.table(wide_data)

wide_data$date <- paste(wide_data$date, wide_data$hour)

production_data <- read.csv('data/2022-05-30_production.csv')
production_data <- data.table(production_data)

production_data$date <- paste(production_data$date, production_data$hour)
production_data <- production_data[,-c(2)]

wide_data$date <- as.POSIXct(wide_data$date,format="%Y-%m-%d %H",tz=Sys.timezone(),tryFormat="%Y-%m-%d %H")
production_data$date <- as.POSIXct(production_data$date,format="%Y-%m-%d %H",tz=Sys.timezone(),tryFormat="%Y-%m-%d %H")

MatrixA <- merge(wide_data, production_data, by="date")

MatrixA <- rbind(MatrixA,wide_data[11569:11592,],fill=TRUE)

Stationarity of the data

MatrixA[,differ:=production]
ggplot(MatrixA,aes(x=date)) + geom_line(aes(y=differ))
unt_test=ur.kpss(MatrixA$differ) 
summary(unt_test)

Warning message:
“Removed 24 row(s) containing missing values (geom_path).”

####################### 
# KPSS Unit Root Test # 
####################### 

Test is of type: mu with 13 lags. 

Value of test-statistic is: 2.8241 

Critical value for a significance level of: 
                10pct  5pct 2.5pct  1pct
critical values 0.347 0.463  0.574 0.739

acf(MatrixA[complete.cases(MatrixA)]$differ)
pacf(MatrixA[complete.cases(MatrixA)]$differ)

Value of test-statistic is too high which means data is not stationary. As it can be seen from the lag 24 we should shift it 24 lags

MatrixA[,differ:=production-shift(production,24)]
ggplot(MatrixA,aes(x=date)) + geom_line(aes(y=differ))
unt_test=ur.kpss(MatrixA$differ) 
summary(unt_test)

Warning message:
“Removed 48 row(s) containing missing values (geom_path).”

####################### 
# KPSS Unit Root Test # 
####################### 

Test is of type: mu with 13 lags. 

Value of test-statistic is: 0.0122 

Critical value for a significance level of: 
                10pct  5pct 2.5pct  1pct
critical values 0.347 0.463  0.574 0.739

Now the value of test-statistic is low enough which means the data is stationary now.

require(forecast)
acf(MatrixA[complete.cases(MatrixA)]$differ)
pacf(MatrixA[complete.cases(MatrixA)]$differ)
fitted=auto.arima(MatrixA$differ,seasonal=,F,trace=T,stepwise=F,approximation=F)

 ARIMA(0,0,0) with zero mean     : 73214.34
 ARIMA(0,0,0) with non-zero mean : 73216.05
 ARIMA(0,0,1) with zero mean     : 66464.01
 ARIMA(0,0,1) with non-zero mean : 66465.82
 ARIMA(0,0,2) with zero mean     : 64552.05
 ARIMA(0,0,2) with non-zero mean : 64553.92
 ARIMA(0,0,3) with zero mean     : 63843.9
 ARIMA(0,0,3) with non-zero mean : 63845.8
 ARIMA(0,0,4) with zero mean     : 63638.43
 ARIMA(0,0,4) with non-zero mean : 63640.35
 ARIMA(0,0,5) with zero mean     : 63540.96
 ARIMA(0,0,5) with non-zero mean : 63542.89
 ARIMA(1,0,0) with zero mean     : 63600.86
 ARIMA(1,0,0) with non-zero mean : 63602.82
 ARIMA(1,0,1) with zero mean     : 63417.09
 ARIMA(1,0,1) with non-zero mean : 63419.04
 ARIMA(1,0,2) with zero mean     : 63417.73
 ARIMA(1,0,2) with non-zero mean : 63419.68
 ARIMA(1,0,3) with zero mean     : 63419.4
 ARIMA(1,0,3) with non-zero mean : 63421.35
 ARIMA(1,0,4) with zero mean     : 63418.54
 ARIMA(1,0,4) with non-zero mean : 63420.49
 ARIMA(2,0,0) with zero mean     : 63427.88
 ARIMA(2,0,0) with non-zero mean : 63429.82
 ARIMA(2,0,1) with zero mean     : 63417.83
 ARIMA(2,0,1) with non-zero mean : 63419.78
 ARIMA(2,0,2) with zero mean     : 63419.73
 ARIMA(2,0,2) with non-zero mean : 63421.68
 ARIMA(2,0,3) with zero mean     : Inf
 ARIMA(2,0,3) with non-zero mean : Inf
 ARIMA(3,0,0) with zero mean     : 63417.14
 ARIMA(3,0,0) with non-zero mean : 63419.09
 ARIMA(3,0,1) with zero mean     : 63420.37
 ARIMA(3,0,1) with non-zero mean : 63421.98
 ARIMA(3,0,2) with zero mean     : 63421.69
 ARIMA(3,0,2) with non-zero mean : 63423.63
 ARIMA(4,0,0) with zero mean     : 63419
 ARIMA(4,0,0) with non-zero mean : 63420.95
 ARIMA(4,0,1) with zero mean     : 63420.8
 ARIMA(4,0,1) with non-zero mean : 63422.76
 ARIMA(5,0,0) with zero mean     : 63419.29
 ARIMA(5,0,0) with non-zero mean : 63421.24



 Best model: ARIMA(1,0,1) with zero mean     

Linear Models

#linear
night<-(c(21,22,23,0,1,2,3))

hourly_production=MatrixA
hourly_production[,trend:=1:.N]
hourly_production[,w_hour:=hour]
hourly_production[,mon:=as.character(month(date,label=T))]
hourly_production[,av_dswrf:=(DSWRF_36.25_33+DSWRF_36.25_33.25+DSWRF_36.25_33.5+DSWRF_36.5_33+DSWRF_36.5_33.25+DSWRF_36.5_33.5+DSWRF_36.75_33+DSWRF_36.75_33.25+DSWRF_36.75_33.5)/9]
hourly_production[,av_cloud:=(CLOUD_LOW_LAYER_36.25_33+CLOUD_LOW_LAYER_36.25_33.25+CLOUD_LOW_LAYER_36.25_33.5+CLOUD_LOW_LAYER_36.5_33+CLOUD_LOW_LAYER_36.5_33.25+CLOUD_LOW_LAYER_36.5_33.5+CLOUD_LOW_LAYER_36.75_33+CLOUD_LOW_LAYER_36.75_33.25+CLOUD_LOW_LAYER_36.75_33.5)/9]
hourly_production[,av_temp:=(TEMP_36.25_33+TEMP_36.25_33.25+TEMP_36.25_33.5+TEMP_36.5_33+TEMP_36.5_33.25+TEMP_36.5_33.5+TEMP_36.75_33+TEMP_36.75_33.25+TEMP_36.75_33.5)/9]
hourly_production[,av_hum:=(REL_HUMIDITY_36.25_33+REL_HUMIDITY_36.25_33.25+REL_HUMIDITY_36.25_33.5+REL_HUMIDITY_36.5_33+REL_HUMIDITY_36.5_33.25+REL_HUMIDITY_36.5_33.5+REL_HUMIDITY_36.75_33+REL_HUMIDITY_36.75_33.25+REL_HUMIDITY_36.75_33.5)/9]

hourly_production[,is_night:=as.numeric(hour %in% night)]
hourly_production[,lag_24:=shift(production,24)]
hourly_production[,differ:=production-lag_24]

Trend: There seems to be a small trend that we think is due to global warming, so we added the trend to our model. In the light of this metric, we can calculate the linear increase in the amount of solar energy production.

is_night: This parameter allows us to distinguish between day and night so that we can easily exclude the 0 values at night in the solar energy production table. In this way, the values between ..am- .. pm is excluded.

w_hour: This metric provides the opportunity to integrate the day-time breakdown of the given data into the model and to differentiate on the basis of day and hour. Since the weather does not change very rapidly, there is no significant difference in energy production from a few days ago. Because of this situation, we used the lagged variables from a few days ago.

av_temp: This metric calculates the average of the temperature amounts for 9 grid points

av_dswrf: This metric calculates the average of the DSWRF values for 9 grid points

av_cloud: This metric calculates the average of the cloud rates for 9 grid points

av_hum: This metric calculates the average of the humidity amounts for 9 grid points

forecast_with_lr=function(fmla, data,forecast_data){
    fitted_lm=lm(as.formula(fmla),data)
    forecasted4=predict(fitted_lm,forecast_data)
    return(list(forecast=as.numeric(forecasted4),model=fitted_lm))
}

#linear regression with only trend w_hour and is_night


    
    past_data=hourly_production[1:11424]
    forecast_data=hourly_production[11425:11448]
    
   



    diff_fmla='differ~trend+w_hour+is_night'
    forecasted4=forecast_with_lr(diff_fmla,past_data,forecast_data)
    forecast_data[,lm_differ_prediction:=forecasted4$forecast+lag_24]

    

forecast_data

A data.table: 24 × 46

date	hour	CLOUD_LOW_LAYER_36.25_33	CLOUD_LOW_LAYER_36.25_33.25	CLOUD_LOW_LAYER_36.25_33.5	CLOUD_LOW_LAYER_36.5_33	CLOUD_LOW_LAYER_36.5_33.25	CLOUD_LOW_LAYER_36.5_33.5	CLOUD_LOW_LAYER_36.75_33	CLOUD_LOW_LAYER_36.75_33.25	⋯	TEMP_36.75_33.25	TEMP_36.75_33.5	production	differ	trend	w_hour	mon	is_night	lag_24	lm_differ_prediction
<dttm>	<int>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	⋯	<dbl>	<dbl>	<dbl>	<dbl>	<int>	<int>	<chr>	<dbl>	<dbl>	<dbl>
2022-05-29 00:00:00	0	0.6	0.0	0	1.0	0.0	0	0.1	0.3	⋯	295.283	293.183	NA	NA	11425	0	May	1	0.00	-0.02985092
2022-05-29 01:00:00	1	0.4	0.0	0	0.7	0.0	0	0.1	0.2	⋯	294.897	292.897	NA	NA	11426	1	May	1	0.00	-0.02999798
2022-05-29 02:00:00	2	0.4	0.0	0	0.6	0.0	0	0.1	0.2	⋯	294.311	292.611	NA	NA	11427	2	May	1	0.00	-0.03014504
2022-05-29 03:00:00	3	0.3	0.0	0	0.4	0.0	0	0.1	0.2	⋯	293.918	292.318	NA	NA	11428	3	May	1	0.00	-0.03029210
2022-05-29 04:00:00	4	0.0	0.0	0	0.0	0.0	0	0.0	0.0	⋯	293.641	292.041	NA	NA	11429	4	May	0	0.00	0.01278396
2022-05-29 05:00:00	5	0.0	0.0	0	0.0	0.0	0	0.0	0.0	⋯	293.141	291.741	NA	NA	11430	5	May	0	0.15	0.16263690
2022-05-29 06:00:00	6	0.0	0.0	0	0.0	0.0	0	0.0	0.0	⋯	293.359	291.859	NA	NA	11431	6	May	0	6.99	7.00248984
2022-05-29 07:00:00	7	0.0	0.0	0	0.0	0.0	0	0.0	0.0	⋯	296.259	294.359	NA	NA	11432	7	May	0	26.05	26.06234278
2022-05-29 08:00:00	8	0.0	0.0	0	0.0	0.0	0	0.0	0.0	⋯	298.000	296.200	NA	NA	11433	8	May	0	35.00	35.01219572
2022-05-29 09:00:00	9	0.0	0.0	0	0.0	0.0	0	0.0	0.0	⋯	299.314	297.414	NA	NA	11434	9	May	0	35.00	35.01204866
2022-05-29 10:00:00	10	0.0	0.0	0	0.0	0.0	0	0.0	0.0	⋯	300.406	298.406	NA	NA	11435	10	May	0	35.00	35.01190160
2022-05-29 11:00:00	11	0.0	0.0	0	0.0	0.0	0	0.0	0.0	⋯	301.488	299.388	NA	NA	11436	11	May	0	35.00	35.01175454
2022-05-29 12:00:00	12	0.0	0.0	0	0.0	0.0	0	0.0	0.0	⋯	302.424	300.224	NA	NA	11437	12	May	0	35.00	35.01160748
2022-05-29 13:00:00	13	0.0	0.0	0	0.0	0.0	0	0.0	0.0	⋯	303.357	301.157	NA	NA	11438	13	May	0	35.00	35.01146042
2022-05-29 14:00:00	14	0.0	0.7	0	0.0	0.0	0	0.0	0.0	⋯	303.957	301.757	NA	NA	11439	14	May	0	35.00	35.01131336
2022-05-29 15:00:00	15	0.0	0.5	0	0.0	0.0	0	0.0	0.0	⋯	304.436	302.236	NA	NA	11440	15	May	0	32.60	32.61116630
2022-05-29 16:00:00	16	0.0	0.0	0	0.0	0.0	0	0.0	0.0	⋯	304.739	301.439	NA	NA	11441	16	May	0	26.20	26.21101923
2022-05-29 17:00:00	17	0.0	0.0	0	0.0	0.0	0	2.2	0.5	⋯	303.494	299.994	NA	NA	11442	17	May	0	20.97	20.98087217
2022-05-29 18:00:00	18	0.0	0.0	0	1.1	0.1	0	3.1	0.7	⋯	302.094	298.994	NA	NA	11443	18	May	0	9.47	9.48072511
2022-05-29 19:00:00	19	0.0	0.0	0	1.6	0.1	0	2.9	0.5	⋯	300.802	297.902	NA	NA	11444	19	May	0	1.23	1.24057805
2022-05-29 20:00:00	20	0.0	0.0	0	1.3	0.1	0	2.4	0.4	⋯	298.600	295.800	NA	NA	11445	20	May	0	0.00	0.01043099
2022-05-29 21:00:00	21	0.0	0.0	0	1.1	0.0	0	2.0	0.4	⋯	297.329	295.229	NA	NA	11446	21	May	1	0.00	-0.03293919
2022-05-29 22:00:00	22	0.0	0.0	0	0.0	0.0	0	0.0	0.0	⋯	296.685	294.785	NA	NA	11447	22	May	1	0.00	-0.03308625
2022-05-29 23:00:00	23	0.0	0.0	0	0.0	0.0	0	0.0	0.0	⋯	296.007	294.107	NA	NA	11448	23	May	1	0.00	-0.03323332

#linear regression with all average variables 
    
    
    past_data=hourly_production[1:11424]
    forecast_data=hourly_production[11425:11448]
    
   



    diff_fmla='differ~trend+w_hour+is_night+av_dswrf+av_temp+av_hum+av_cloud'
    forecasted4=forecast_with_lr(diff_fmla,past_data,forecast_data)
    forecast_data[,lm_differ_prediction:=forecasted4$forecast+lag_24]

    

forecast_data

A data.table: 24 × 50

date	hour	CLOUD_LOW_LAYER_36.25_33	CLOUD_LOW_LAYER_36.25_33.25	CLOUD_LOW_LAYER_36.25_33.5	CLOUD_LOW_LAYER_36.5_33	CLOUD_LOW_LAYER_36.5_33.25	CLOUD_LOW_LAYER_36.5_33.5	CLOUD_LOW_LAYER_36.75_33	CLOUD_LOW_LAYER_36.75_33.25	⋯	trend	w_hour	mon	is_night	lag_24	av_dswrf	av_cloud	av_temp	av_hum	lm_differ_prediction
<dttm>	<int>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	⋯	<int>	<int>	<chr>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>
2022-05-29 00:00:00	0	0.6	0.0	0	1.0	0.0	0	0.1	0.3	⋯	11425	0	May	1	0.00	0.000000	0.35555556	293.9497	39.14444	-0.32950719
2022-05-29 01:00:00	1	0.4	0.0	0	0.7	0.0	0	0.1	0.2	⋯	11426	1	May	1	0.00	0.000000	0.24444444	293.7748	38.88889	-0.31304136
2022-05-29 02:00:00	2	0.4	0.0	0	0.6	0.0	0	0.1	0.2	⋯	11427	2	May	1	0.00	0.000000	0.22222222	293.4999	39.48889	-0.28773760
2022-05-29 03:00:00	3	0.3	0.0	0	0.4	0.0	0	0.1	0.2	⋯	11428	3	May	1	0.00	0.000000	0.17777778	293.1624	39.97778	-0.25629172
2022-05-29 04:00:00	4	0.0	0.0	0	0.0	0.0	0	0.0	0.0	⋯	11429	4	May	0	0.00	0.000000	0.00000000	292.7077	42.17778	-0.44061800
2022-05-29 05:00:00	5	0.0	0.0	0	0.0	0.0	0	0.0	0.0	⋯	11430	5	May	0	0.15	0.000000	0.00000000	292.4632	42.77778	-0.26908065
2022-05-29 06:00:00	6	0.0	0.0	0	0.0	0.0	0	0.0	0.0	⋯	11431	6	May	0	6.99	1.931111	0.00000000	292.7034	43.85556	6.55549104
2022-05-29 07:00:00	7	0.0	0.0	0	0.0	0.0	0	0.0	0.0	⋯	11432	7	May	0	26.05	30.424444	0.00000000	295.5257	38.63333	25.39962305
2022-05-29 08:00:00	8	0.0	0.0	0	0.0	0.0	0	0.0	0.0	⋯	11433	8	May	0	35.00	87.006222	0.00000000	297.3778	32.16667	34.27973182
2022-05-29 09:00:00	9	0.0	0.0	0	0.0	0.0	0	0.0	0.0	⋯	11434	9	May	0	35.00	158.960000	0.00000000	298.6696	29.81111	34.31450830
2022-05-29 10:00:00	10	0.0	0.0	0	0.0	0.0	0	0.0	0.0	⋯	11435	10	May	0	35.00	706.260000	0.00000000	299.7616	27.48889	35.45807716
2022-05-29 11:00:00	11	0.0	0.0	0	0.0	0.0	0	0.0	0.0	⋯	11436	11	May	0	35.00	781.066667	0.00000000	300.6213	26.58889	35.54498675
2022-05-29 12:00:00	12	0.0	0.0	0	0.0	0.0	0	0.0	0.0	⋯	11437	12	May	0	35.00	839.615556	0.03333333	301.3018	25.28889	35.60733861
2022-05-29 13:00:00	13	0.0	0.0	0	0.0	0.0	0	0.0	0.0	⋯	11438	13	May	0	35.00	879.955556	0.02222222	302.0903	23.44444	35.61772506
2022-05-29 14:00:00	14	0.0	0.7	0	0.0	0.0	0	0.0	0.0	⋯	11439	14	May	0	35.00	900.953333	0.10000000	302.4681	23.00000	35.62304298
2022-05-29 15:00:00	15	0.0	0.5	0	0.0	0.0	0	0.0	0.0	⋯	11440	15	May	0	32.60	899.205333	0.07777778	302.5138	23.55556	33.21529193
2022-05-29 16:00:00	16	0.0	0.0	0	0.0	0.0	0	0.0	0.0	⋯	11441	16	May	0	26.20	747.962222	0.00000000	302.1057	24.76667	26.51095000
2022-05-29 17:00:00	17	0.0	0.0	0	0.0	0.0	0	2.2	0.5	⋯	11442	17	May	0	20.97	643.155556	0.30000000	301.1718	27.10000	21.11817237
2022-05-29 18:00:00	18	0.0	0.0	0	1.1	0.1	0	3.1	0.7	⋯	11443	18	May	0	9.47	547.082222	0.55555556	300.3162	29.08889	9.46884996
2022-05-29 19:00:00	19	0.0	0.0	0	1.6	0.1	0	2.9	0.5	⋯	11444	19	May	0	1.23	457.420000	0.56666667	299.1576	32.68889	1.14025000
2022-05-29 20:00:00	20	0.0	0.0	0	1.3	0.1	0	2.4	0.4	⋯	11445	20	May	0	0.00	373.395556	0.46666667	296.2333	40.02222	0.01580346
2022-05-29 21:00:00	21	0.0	0.0	0	1.1	0.0	0	2.0	0.4	⋯	11446	21	May	1	0.00	311.162667	0.38888889	295.5068	40.96667	0.18350520
2022-05-29 22:00:00	22	0.0	0.0	0	0.0	0.0	0	0.0	0.0	⋯	11447	22	May	1	0.00	0.000000	0.00000000	295.1517	40.05556	-0.48795142
2022-05-29 23:00:00	23	0.0	0.0	0	0.0	0.0	0	0.0	0.0	⋯	11448	23	May	1	0.00	0.000000	0.00000000	294.7292	40.51111	-0.45106739

#linear regression with all average variables except w_hour(hourly seaonality)
    
    
    past_data=hourly_production[1:11424]
    forecast_data=hourly_production[11425:11448]
    
   



    diff_fmla='differ~trend+is_night+av_dswrf+av_temp+av_hum+av_cloud'
    forecasted4=forecast_with_lr(diff_fmla,past_data,forecast_data)
    forecast_data[,lm_differ_prediction:=forecasted4$forecast+lag_24]

    

forecast_data

A data.table: 24 × 50

date	hour	CLOUD_LOW_LAYER_36.25_33	CLOUD_LOW_LAYER_36.25_33.25	CLOUD_LOW_LAYER_36.25_33.5	CLOUD_LOW_LAYER_36.5_33	CLOUD_LOW_LAYER_36.5_33.25	CLOUD_LOW_LAYER_36.5_33.5	CLOUD_LOW_LAYER_36.75_33	CLOUD_LOW_LAYER_36.75_33.25	⋯	trend	w_hour	mon	is_night	lag_24	av_dswrf	av_cloud	av_temp	av_hum	lm_differ_prediction
<dttm>	<int>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	⋯	<int>	<int>	<chr>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>
2022-05-29 00:00:00	0	0.6	0.0	0	1.0	0.0	0	0.1	0.3	⋯	11425	0	May	1	0.00	0.000000	0.35555556	293.9497	39.14444	-0.36084816
2022-05-29 01:00:00	1	0.4	0.0	0	0.7	0.0	0	0.1	0.2	⋯	11426	1	May	1	0.00	0.000000	0.24444444	293.7748	38.88889	-0.34110059
2022-05-29 02:00:00	2	0.4	0.0	0	0.6	0.0	0	0.1	0.2	⋯	11427	2	May	1	0.00	0.000000	0.22222222	293.4999	39.48889	-0.31256381
2022-05-29 03:00:00	3	0.3	0.0	0	0.4	0.0	0	0.1	0.2	⋯	11428	3	May	1	0.00	0.000000	0.17777778	293.1624	39.97778	-0.27787107
2022-05-29 04:00:00	4	0.0	0.0	0	0.0	0.0	0	0.0	0.0	⋯	11429	4	May	0	0.00	0.000000	0.00000000	292.7077	42.17778	-0.45448629
2022-05-29 05:00:00	5	0.0	0.0	0	0.0	0.0	0	0.0	0.0	⋯	11430	5	May	0	0.15	0.000000	0.00000000	292.4632	42.77778	-0.27972077
2022-05-29 06:00:00	6	0.0	0.0	0	0.0	0.0	0	0.0	0.0	⋯	11431	6	May	0	6.99	1.931111	0.00000000	292.7034	43.85556	6.54794600
2022-05-29 07:00:00	7	0.0	0.0	0	0.0	0.0	0	0.0	0.0	⋯	11432	7	May	0	26.05	30.424444	0.00000000	295.5257	38.63333	25.39441103
2022-05-29 08:00:00	8	0.0	0.0	0	0.0	0.0	0	0.0	0.0	⋯	11433	8	May	0	35.00	87.006222	0.00000000	297.3778	32.16667	34.27605605
2022-05-29 09:00:00	9	0.0	0.0	0	0.0	0.0	0	0.0	0.0	⋯	11434	9	May	0	35.00	158.960000	0.00000000	298.6696	29.81111	34.31166611
2022-05-29 10:00:00	10	0.0	0.0	0	0.0	0.0	0	0.0	0.0	⋯	11435	10	May	0	35.00	706.260000	0.00000000	299.7616	27.48889	35.44002701
2022-05-29 11:00:00	11	0.0	0.0	0	0.0	0.0	0	0.0	0.0	⋯	11436	11	May	0	35.00	781.066667	0.00000000	300.6213	26.58889	35.52762865
2022-05-29 12:00:00	12	0.0	0.0	0	0.0	0.0	0	0.0	0.0	⋯	11437	12	May	0	35.00	839.615556	0.03333333	301.3018	25.28889	35.59125594
2022-05-29 13:00:00	13	0.0	0.0	0	0.0	0.0	0	0.0	0.0	⋯	11438	13	May	0	35.00	879.955556	0.02222222	302.0903	23.44444	35.60355888
2022-05-29 14:00:00	14	0.0	0.7	0	0.0	0.0	0	0.0	0.0	⋯	11439	14	May	0	35.00	900.953333	0.10000000	302.4681	23.00000	35.61139369
2022-05-29 15:00:00	15	0.0	0.5	0	0.0	0.0	0	0.0	0.0	⋯	11440	15	May	0	32.60	899.205333	0.07777778	302.5138	23.55556	33.20691007
2022-05-29 16:00:00	16	0.0	0.0	0	0.0	0.0	0	0.0	0.0	⋯	11441	16	May	0	26.20	747.962222	0.00000000	302.1057	24.76667	26.51089263
2022-05-29 17:00:00	17	0.0	0.0	0	0.0	0.0	0	2.2	0.5	⋯	11442	17	May	0	20.97	643.155556	0.30000000	301.1718	27.10000	21.12481364
2022-05-29 18:00:00	18	0.0	0.0	0	1.1	0.1	0	3.1	0.7	⋯	11443	18	May	0	9.47	547.082222	0.55555556	300.3162	29.08889	9.48191216
2022-05-29 19:00:00	19	0.0	0.0	0	1.6	0.1	0	2.9	0.5	⋯	11444	19	May	0	1.23	457.420000	0.56666667	299.1576	32.68889	1.15947683
2022-05-29 20:00:00	20	0.0	0.0	0	1.3	0.1	0	2.4	0.4	⋯	11445	20	May	0	0.00	373.395556	0.46666667	296.2333	40.02222	0.04095573
2022-05-29 21:00:00	21	0.0	0.0	0	1.1	0.0	0	2.0	0.4	⋯	11446	21	May	1	0.00	311.162667	0.38888889	295.5068	40.96667	0.20948057
2022-05-29 22:00:00	22	0.0	0.0	0	0.0	0.0	0	0.0	0.0	⋯	11447	22	May	1	0.00	0.000000	0.00000000	295.1517	40.05556	-0.44810305
2022-05-29 23:00:00	23	0.0	0.0	0	0.0	0.0	0	0.0	0.0	⋯	11448	23	May	1	0.00	0.000000	0.00000000	294.7292	40.51111	-0.40796766

ARIMA Models

ARIMA with all variables

#all variables
fitted
nahead=24
reg_matrix=cbind(MatrixA$TEMP_36.25_33,MatrixA$TEMP_36.25_33.25,MatrixA$TEMP_36.25_33.5,MatrixA$TEMP_36.5_33,MatrixA$TEMP_36.5_33.25,MatrixA$TEMP_36.5_33.5,MatrixA$TEMP_36.75_33,MatrixA$TEMP_36.75_33.25,MatrixA$TEMP_36.75_33.5,MatrixA$CLOUD_LOW_LAYER_36.25_33,MatrixA$CLOUD_LOW_LAYER_36.25_33.25,MatrixA$CLOUD_LOW_LAYER_36.25_33.5,MatrixA$CLOUD_LOW_LAYER_36.5_33,MatrixA$CLOUD_LOW_LAYER_36.5_33.25,MatrixA$CLOUD_LOW_LAYER_36.5_33.5,MatrixA$CLOUD_LOW_LAYER_36.75_33,MatrixA$CLOUD_LOW_LAYER_36.75_33.25,MatrixA$CLOUD_LOW_LAYER_36.75_33.5,MatrixA$REL_HUMIDITY_36.25_33,MatrixA$REL_HUMIDITY_36.25_33.25,MatrixA$REL_HUMIDITY_36.25_33.5,MatrixA$REL_HUMIDITY_36.5_33,MatrixA$REL_HUMIDITY_36.5_33.25,MatrixA$REL_HUMIDITY_36.5_33.5,MatrixA$REL_HUMIDITY_36.75_33,MatrixA$REL_HUMIDITY_36.75_33.25,MatrixA$REL_HUMIDITY_36.75_33.5,MatrixA$DSWRF_36.25_33,MatrixA$DSWRF_36.25_33.25,MatrixA$DSWRF_36.25_33.5,MatrixA$DSWRF_36.5_33,MatrixA$DSWRF_36.5_33.25,MatrixA$DSWRF_36.5_33.5,MatrixA$DSWRF_36.75_33,MatrixA$DSWRF_36.75_33.25,MatrixA$DSWRF_36.75_33.5) 
fitted_arimax=auto.arima(MatrixA$differ,xreg=reg_matrix,seasonal=F,trace=T,stepwise=F,approximation=F)

forecasted1=forecast(fitted_arimax,xreg=tail(reg_matrix,24),  h=24)
forecasted1

Series: MatrixA$differ 
ARIMA(1,0,1) with zero mean 

Coefficients:
         ar1     ma1
      0.6822  0.1712
s.e.  0.0090  0.0122

sigma^2 = 15.25:  log likelihood = -31705.54
AIC=63417.08   AICc=63417.09   BIC=63439.11

 ARIMA(0,0,0) with zero mean     : 72637.67
 ARIMA(0,0,0) with non-zero mean : 72631.69
 ARIMA(0,0,1) with zero mean     : 66144.91
 ARIMA(0,0,1) with non-zero mean : 66139.19
 ARIMA(0,0,2) with zero mean     : 64360.12
 ARIMA(0,0,2) with non-zero mean : 64354.12
 ARIMA(0,0,3) with zero mean     : 63718.69
 ARIMA(0,0,3) with non-zero mean : 63712.65
 ARIMA(0,0,4) with zero mean     : 63540.03
 ARIMA(0,0,4) with non-zero mean : 63534.7
 ARIMA(0,0,5) with zero mean     : 63455.17
 ARIMA(0,0,5) with non-zero mean : 63450.83
 ARIMA(1,0,0) with zero mean     : 63554.43
 ARIMA(1,0,0) with non-zero mean : 63551.72
 ARIMA(1,0,1) with zero mean     : 63360.93
 ARIMA(1,0,1) with non-zero mean : 63357.27
 ARIMA(1,0,2) with zero mean     : 63362.47
 ARIMA(1,0,2) with non-zero mean : 63358.88
 ARIMA(1,0,3) with zero mean     : 63364.45
 ARIMA(1,0,3) with non-zero mean : 63360.86
 ARIMA(1,0,4) with zero mean     : 63364.23
 ARIMA(1,0,4) with non-zero mean : 63360.59
 ARIMA(2,0,0) with zero mean     : 63370.37
 ARIMA(2,0,0) with non-zero mean : 63366.53
 ARIMA(2,0,1) with zero mean     : 63362.48
 ARIMA(2,0,1) with non-zero mean : 63358.89
 ARIMA(2,0,2) with zero mean     : Inf
 ARIMA(2,0,2) with non-zero mean : Inf
 ARIMA(2,0,3) with zero mean     : 63366.13
 ARIMA(2,0,3) with non-zero mean : 63362.53
 ARIMA(3,0,0) with zero mean     : 63362.37
 ARIMA(3,0,0) with non-zero mean : 63358.78
 ARIMA(3,0,1) with zero mean     : 63364.6
 ARIMA(3,0,1) with non-zero mean : 63360.98
 ARIMA(3,0,2) with zero mean     : 63366.19
 ARIMA(3,0,2) with non-zero mean : 63362.59
 ARIMA(4,0,0) with zero mean     : 63364.38
 ARIMA(4,0,0) with non-zero mean : 63360.79
 ARIMA(4,0,1) with zero mean     : 63365.7
 ARIMA(4,0,1) with non-zero mean : 63362.12
 ARIMA(5,0,0) with zero mean     : 63365.26
 ARIMA(5,0,0) with non-zero mean : 63361.63



 Best model: Regression with ARIMA(1,0,1) errors 

      Point Forecast     Lo 80    Hi 80     Lo 95    Hi 95
11449    -0.23985392 -7.783281 7.303573 -11.77653 11.29682
11450    -0.22361060 -7.767038 7.319817 -11.76029 11.31307
11451    -0.20814707 -7.751574 7.335280 -11.74482 11.32853
11452    -0.27234178 -7.815769 7.271086 -11.80902 11.26433
11453    -0.23733378 -7.780761 7.306094 -11.77401 11.29934
11454    -0.18865640 -7.732084 7.354771 -11.72533 11.34802
11455    -0.22368016 -7.767108 7.319747 -11.76036 11.31300
11456    -0.12170396 -7.665131 7.421723 -11.65838 11.41497
11457    -0.11418910 -7.657616 7.429238 -11.65087 11.42249
11458    -0.13827462 -7.681702 7.405153 -11.67495 11.39840
11459     0.14588678 -7.397541 7.689314 -11.39079 11.68256
11460     0.15793433 -7.385493 7.701362 -11.37874 11.69461
11461     0.14613707 -7.397290 7.689564 -11.39054 11.68281
11462     0.10867346 -7.434754 7.652101 -11.42800 11.64535
11463    -0.06957341 -7.613001 7.473854 -11.60625 11.46710
11464    -0.35206589 -7.895493 7.191361 -11.88874 11.18461
11465    -1.41030541 -8.953733 6.133122 -12.94698 10.12637
11466    -1.09452271 -8.637950 6.448905 -12.63120 10.44215
11467    -1.39384236 -8.937270 6.149585 -12.93052 10.14283
11468    -1.31873902 -8.862166 6.224688 -12.85542 10.21794
11469    -0.96778364 -8.511211 6.575644 -12.50446 10.56889
11470    -0.69214255 -8.235570 6.851285 -12.22882 10.84453
11471    -0.06632151 -7.609749 7.477106 -11.60300 11.47036
11472    -0.07023206 -7.613659 7.473195 -11.60691 11.46644

temporary1=copy(MatrixA)

temporary1[,predicted_differ:=differ] 

test1=MatrixA[11425:11448]
test1[,production:=NA]
test1[,predicted_differ:=as.numeric(forecasted1$mean)]

temporary1[11425:11448]=test1


temporary1[,forecastval:=predicted_differ+shift(production,24)]
temporary1[11400:11450,]

A data.table: 51 × 42

date	hour	CLOUD_LOW_LAYER_36.25_33	CLOUD_LOW_LAYER_36.25_33.25	CLOUD_LOW_LAYER_36.25_33.5	CLOUD_LOW_LAYER_36.5_33	CLOUD_LOW_LAYER_36.5_33.25	CLOUD_LOW_LAYER_36.5_33.5	CLOUD_LOW_LAYER_36.75_33	CLOUD_LOW_LAYER_36.75_33.25	⋯	TEMP_36.5_33	TEMP_36.5_33.25	TEMP_36.5_33.5	TEMP_36.75_33	TEMP_36.75_33.25	TEMP_36.75_33.5	production	differ	predicted_differ	forecastval
<dttm>	<int>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	⋯	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>
2022-05-27 23:00:00	23	3.6	0.3	0.0	0.0	1.8	2.3	3.4	4.1	⋯	290.951	293.551	296.651	289.651	294.351	292.751	0.00	0.00	0.00000000	0.00000000
2022-05-28 00:00:00	0	4.0	0.3	0.0	0.6	1.2	1.6	2.2	3.7	⋯	290.396	293.396	295.796	289.396	293.596	291.896	0.00	0.00	0.00000000	0.00000000
2022-05-28 01:00:00	1	3.7	0.6	0.0	0.4	0.9	1.1	1.7	2.8	⋯	289.702	292.802	295.302	288.902	293.202	291.602	0.00	0.00	0.00000000	0.00000000
2022-05-28 02:00:00	2	3.4	0.5	0.0	0.4	1.7	0.9	1.4	2.2	⋯	289.317	292.517	294.917	288.617	293.017	291.417	0.00	0.00	0.00000000	0.00000000
2022-05-28 03:00:00	3	3.3	0.4	0.0	0.4	1.4	0.8	1.2	1.9	⋯	289.051	292.251	294.551	288.351	292.751	291.051	0.00	0.00	0.00000000	0.00000000
2022-05-28 04:00:00	4	0.0	0.0	0.0	0.0	3.4	0.0	0.0	0.0	⋯	288.568	291.968	293.968	287.868	292.168	290.568	0.00	0.00	0.00000000	0.00000000
2022-05-28 05:00:00	5	0.0	0.0	0.0	0.0	1.7	0.0	0.0	0.0	⋯	288.282	291.582	293.482	287.682	291.782	290.282	0.15	-0.06	-0.06000000	0.15000000
2022-05-28 06:00:00	6	0.0	0.0	0.0	0.0	1.2	0.0	0.0	0.3	⋯	288.366	291.666	293.866	287.566	291.766	290.166	6.99	0.19	0.19000000	6.99000000
2022-05-28 07:00:00	7	0.0	0.0	0.0	0.0	0.8	0.0	0.0	1.1	⋯	290.111	293.411	296.711	289.011	293.411	291.811	26.05	0.60	0.60000000	26.05000000
2022-05-28 08:00:00	8	0.0	0.0	0.0	0.0	0.7	0.0	0.1	1.5	⋯	291.800	295.300	298.500	290.900	295.700	294.200	35.00	0.00	0.00000000	35.00000000
2022-05-28 09:00:00	9	0.0	0.0	0.0	0.0	0.5	0.0	0.1	1.2	⋯	293.511	297.011	299.911	292.011	297.311	295.711	35.00	0.00	0.00000000	35.00000000
2022-05-28 10:00:00	10	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	⋯	295.337	298.437	301.637	293.137	298.737	297.037	35.00	0.00	0.00000000	35.00000000
2022-05-28 11:00:00	11	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	⋯	296.250	299.550	303.350	294.050	299.650	297.950	35.00	0.00	0.00000000	35.00000000
2022-05-28 12:00:00	12	0.6	0.0	0.0	0.0	0.0	0.0	0.0	0.0	⋯	297.206	300.406	304.606	294.906	300.406	298.606	35.00	0.00	0.00000000	35.00000000
2022-05-28 13:00:00	13	1.1	0.3	0.0	0.4	0.0	0.0	0.0	0.3	⋯	298.100	301.300	305.500	295.900	301.200	299.400	35.00	0.00	0.00000000	35.00000000
2022-05-28 14:00:00	14	0.9	0.5	0.0	1.3	0.1	0.0	0.0	0.4	⋯	298.700	301.900	306.000	296.500	301.900	299.800	35.00	0.00	0.00000000	35.00000000
2022-05-28 15:00:00	15	8.9	3.5	0.0	1.4	0.1	0.6	0.0	0.5	⋯	297.095	301.495	306.295	297.095	302.495	300.095	32.60	0.12	0.12000000	32.60000000
2022-05-28 16:00:00	16	26.1	18.9	1.5	3.0	1.6	0.0	30.9	4.3	⋯	297.730	300.830	305.430	296.030	301.630	299.830	26.20	22.11	22.11000000	26.20000000
2022-05-28 17:00:00	17	13.1	9.6	0.8	11.7	5.5	0.0	28.8	4.1	⋯	297.632	300.532	305.132	295.432	301.832	298.332	20.97	18.68	18.68000000	20.97000000
2022-05-28 18:00:00	18	9.6	6.8	0.5	26.1	3.8	1.5	26.9	3.2	⋯	296.923	300.623	304.623	294.723	301.123	298.323	9.47	7.33	7.33000000	9.47000000
2022-05-28 19:00:00	19	8.4	5.4	0.5	29.7	4.0	2.1	21.5	3.5	⋯	296.381	300.281	303.181	294.581	300.481	297.381	1.23	0.16	0.16000000	1.23000000
2022-05-28 20:00:00	20	7.7	4.6	0.4	24.2	3.2	1.7	17.2	3.1	⋯	293.800	297.200	300.100	293.100	297.800	295.100	0.00	0.00	0.00000000	0.00000000
2022-05-28 21:00:00	21	6.7	4.0	0.4	20.2	3.3	1.4	14.3	2.7	⋯	292.728	295.828	298.828	291.828	296.028	294.628	0.00	0.00	0.00000000	0.00000000
2022-05-28 22:00:00	22	0.0	0.0	0.0	2.8	0.0	0.0	0.0	0.7	⋯	292.215	295.015	297.615	290.515	295.315	293.815	0.00	0.00	0.00000000	0.00000000
2022-05-28 23:00:00	23	0.9	0.0	0.0	1.4	0.0	0.0	0.0	0.4	⋯	291.642	294.442	297.042	290.042	295.542	293.542	0.00	0.00	0.00000000	0.00000000
2022-05-29 00:00:00	0	0.6	0.0	0.0	1.0	0.0	0.0	0.1	0.3	⋯	291.283	294.383	296.683	289.983	295.283	293.183	NA	NA	-0.23985392	-0.23985392
2022-05-29 01:00:00	1	0.4	0.0	0.0	0.7	0.0	0.0	0.1	0.2	⋯	290.897	294.197	296.097	289.597	294.897	292.897	NA	NA	-0.22361060	-0.22361060
2022-05-29 02:00:00	2	0.4	0.0	0.0	0.6	0.0	0.0	0.1	0.2	⋯	290.411	293.911	295.611	289.411	294.311	292.611	NA	NA	-0.20814707	-0.20814707
2022-05-29 03:00:00	3	0.3	0.0	0.0	0.4	0.0	0.0	0.1	0.2	⋯	290.218	293.518	295.118	289.518	293.918	292.318	NA	NA	-0.27234178	-0.27234178
2022-05-29 04:00:00	4	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	⋯	289.841	293.141	294.741	289.141	293.641	292.041	NA	NA	-0.23733378	-0.23733378
2022-05-29 05:00:00	5	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	⋯	289.541	292.841	294.341	288.941	293.141	291.741	NA	NA	-0.18865640	-0.03865640
2022-05-29 06:00:00	6	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	⋯	289.859	293.159	294.959	289.059	293.359	291.859	NA	NA	-0.22368016	6.76631984
2022-05-29 07:00:00	7	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	⋯	292.959	295.659	298.759	291.359	296.259	294.359	NA	NA	-0.12170396	25.92829604
2022-05-29 08:00:00	8	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	⋯	294.500	297.300	300.300	293.300	298.000	296.200	NA	NA	-0.11418910	34.88581090
2022-05-29 09:00:00	9	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	⋯	296.014	298.714	301.714	294.614	299.314	297.414	NA	NA	-0.13827462	34.86172538
2022-05-29 10:00:00	10	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	⋯	297.406	300.206	303.306	295.706	300.406	298.406	NA	NA	0.14588678	35.14588678
2022-05-29 11:00:00	11	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	⋯	298.488	301.488	304.988	296.588	301.488	299.388	NA	NA	0.15793433	35.15793433
2022-05-29 12:00:00	12	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	⋯	299.524	302.524	306.224	297.524	302.424	300.224	NA	NA	0.14613707	35.14613707
2022-05-29 13:00:00	13	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	⋯	300.357	303.357	306.957	298.357	303.357	301.157	NA	NA	0.10867346	35.10867346
2022-05-29 14:00:00	14	0.0	0.7	0.0	0.0	0.0	0.0	0.0	0.0	⋯	301.157	303.957	307.757	299.057	303.957	301.757	NA	NA	-0.06957341	34.93042659
2022-05-29 15:00:00	15	0.0	0.5	0.0	0.0	0.0	0.0	0.0	0.0	⋯	301.236	303.636	307.236	299.236	304.436	302.236	NA	NA	-0.35206589	32.24793411
2022-05-29 16:00:00	16	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	⋯	300.539	303.139	306.439	298.739	304.739	301.439	NA	NA	-1.41030541	24.78969459
2022-05-29 17:00:00	17	0.0	0.0	0.0	0.0	0.0	0.0	2.2	0.5	⋯	299.694	302.494	305.594	297.094	303.494	299.994	NA	NA	-1.09452271	19.87547729
2022-05-29 18:00:00	18	0.0	0.0	0.0	1.1	0.1	0.0	3.1	0.7	⋯	298.394	301.294	304.794	296.794	302.094	298.994	NA	NA	-1.39384236	8.07615764
2022-05-29 19:00:00	19	0.0	0.0	0.0	1.6	0.1	0.0	2.9	0.5	⋯	297.702	299.502	303.702	296.102	300.802	297.902	NA	NA	-1.31873902	-0.08873902
2022-05-29 20:00:00	20	0.0	0.0	0.0	1.3	0.1	0.0	2.4	0.4	⋯	294.800	297.400	300.600	293.100	298.600	295.800	NA	NA	-0.96778364	-0.96778364
2022-05-29 21:00:00	21	0.0	0.0	0.0	1.1	0.0	0.0	2.0	0.4	⋯	293.729	296.529	299.329	292.029	297.329	295.229	NA	NA	-0.69214255	-0.69214255
2022-05-29 22:00:00	22	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	⋯	293.085	296.385	298.585	291.585	296.685	294.785	NA	NA	-0.06632151	-0.06632151
2022-05-29 23:00:00	23	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	⋯	292.407	295.707	297.707	291.207	296.007	294.107	NA	NA	-0.07023206	-0.07023206
NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	⋯	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	⋯	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA

Error in eval(expr, envir, enclos): object 'results' not found
Traceback:

ARIMA with all variables except temperature variables

#all variables without temp
fitted
nahead=24
reg_matrix2=cbind(MatrixA$CLOUD_LOW_LAYER_36.25_33,MatrixA$CLOUD_LOW_LAYER_36.25_33.25,MatrixA$CLOUD_LOW_LAYER_36.25_33.5,MatrixA$CLOUD_LOW_LAYER_36.5_33,MatrixA$CLOUD_LOW_LAYER_36.5_33.25,MatrixA$CLOUD_LOW_LAYER_36.5_33.5,MatrixA$CLOUD_LOW_LAYER_36.75_33,MatrixA$CLOUD_LOW_LAYER_36.75_33.25,MatrixA$CLOUD_LOW_LAYER_36.75_33.5,MatrixA$REL_HUMIDITY_36.25_33,MatrixA$REL_HUMIDITY_36.25_33.25,MatrixA$REL_HUMIDITY_36.25_33.5,MatrixA$REL_HUMIDITY_36.5_33,MatrixA$REL_HUMIDITY_36.5_33.25,MatrixA$REL_HUMIDITY_36.5_33.5,MatrixA$REL_HUMIDITY_36.75_33,MatrixA$REL_HUMIDITY_36.75_33.25,MatrixA$REL_HUMIDITY_36.75_33.5,MatrixA$DSWRF_36.25_33,MatrixA$DSWRF_36.25_33.25,MatrixA$DSWRF_36.25_33.5,MatrixA$DSWRF_36.5_33,MatrixA$DSWRF_36.5_33.25,MatrixA$DSWRF_36.5_33.5,MatrixA$DSWRF_36.75_33,MatrixA$DSWRF_36.75_33.25,MatrixA$DSWRF_36.75_33.5) 
fitted_arimax2=auto.arima(MatrixA$differ,xreg=reg_matrix2,seasonal=F,trace=T,stepwise=F,approximation=F)

forecasted2=forecast(fitted_arimax2,xreg=tail(reg_matrix2,24),  h=24)
forecasted2

Series: MatrixA$differ 
ARIMA(1,0,1) with zero mean 

Coefficients:
         ar1     ma1
      0.6822  0.1712
s.e.  0.0090  0.0122

sigma^2 = 15.25:  log likelihood = -31705.54
AIC=63417.08   AICc=63417.09   BIC=63439.11

 ARIMA(0,0,0) with zero mean     : 72677.96
 ARIMA(0,0,0) with non-zero mean : 72657.74
 ARIMA(0,0,1) with zero mean     : 66157
 ARIMA(0,0,1) with non-zero mean : 66150.72
 ARIMA(0,0,2) with zero mean     : 64362.02
 ARIMA(0,0,2) with non-zero mean : 64361.14
 ARIMA(0,0,3) with zero mean     : 63710.47
 ARIMA(0,0,3) with non-zero mean : 63711.32
 ARIMA(0,0,4) with zero mean     : 63530
 ARIMA(0,0,4) with non-zero mean : 63531.34
 ARIMA(0,0,5) with zero mean     : 63443.58
 ARIMA(0,0,5) with non-zero mean : 63445.19
 ARIMA(1,0,0) with zero mean     : 63542.7
 ARIMA(1,0,0) with non-zero mean : 63544.54
 ARIMA(1,0,1) with zero mean     : 63348.02
 ARIMA(1,0,1) with non-zero mean : 63350.03
 ARIMA(1,0,2) with zero mean     : 63349.58
 ARIMA(1,0,2) with non-zero mean : 63351.59
 ARIMA(1,0,3) with zero mean     : 63351.58
 ARIMA(1,0,3) with non-zero mean : 63353.6
 ARIMA(1,0,4) with zero mean     : 63351.33
 ARIMA(1,0,4) with non-zero mean : 63353.32
 ARIMA(2,0,0) with zero mean     : 63357.34
 ARIMA(2,0,0) with non-zero mean : 63359.36
 ARIMA(2,0,1) with zero mean     : 63349.59
 ARIMA(2,0,1) with non-zero mean : 63351.59
 ARIMA(2,0,2) with zero mean     : Inf
 ARIMA(2,0,2) with non-zero mean : Inf
 ARIMA(2,0,3) with zero mean     : 63353.16
 ARIMA(2,0,3) with non-zero mean : 63355.16
 ARIMA(3,0,0) with zero mean     : 63349.55
 ARIMA(3,0,0) with non-zero mean : 63351.54
 ARIMA(3,0,1) with zero mean     : 63351.59
 ARIMA(3,0,1) with non-zero mean : 63353.6
 ARIMA(3,0,2) with zero mean     : 63353.22
 ARIMA(3,0,2) with non-zero mean : 63355.23
 ARIMA(4,0,0) with zero mean     : 63351.56
 ARIMA(4,0,0) with non-zero mean : 63353.56
 ARIMA(4,0,1) with zero mean     : 63352.77
 ARIMA(4,0,1) with non-zero mean : 63354.78
 ARIMA(5,0,0) with zero mean     : 63352.44
 ARIMA(5,0,0) with non-zero mean : 63354.43



 Best model: Regression with ARIMA(1,0,1) errors 

      Point Forecast     Lo 80    Hi 80     Lo 95    Hi 95
11449    0.039614943 -7.514384 7.593614 -11.51323 11.59246
11450    0.014967161 -7.539032 7.568966 -11.53788 11.56781
11451   -0.004232844 -7.558232 7.549766 -11.55708 11.54861
11452   -0.034728588 -7.588728 7.519270 -11.58757 11.51812
11453   -0.028218354 -7.582217 7.525781 -11.58106 11.52463
11454   -0.015122822 -7.569122 7.538876 -11.56797 11.53772
11455    0.006461136 -7.547538 7.560460 -11.54638 11.55931
11456    0.177552236 -7.376447 7.731551 -11.37529 11.73040
11457    0.166708669 -7.387290 7.720708 -11.38614 11.71955
11458    0.179643053 -7.374356 7.733642 -11.37320 11.73249
11459    0.403426324 -7.150573 7.957425 -11.14942 11.95627
11460    0.430650144 -7.123349 7.984649 -11.12219 11.98349
11461    0.456701014 -7.097298 8.010700 -11.09614 12.00955
11462    0.468783006 -7.085216 8.022782 -11.08406 12.02163
11463    0.421002362 -7.132997 7.975001 -11.13184 11.97385
11464    0.202609089 -7.351390 7.756608 -11.35024 11.75545
11465   -0.910363105 -8.464362 6.643636 -12.46321 10.64248
11466   -0.682742338 -8.236741 6.871257 -12.23559 10.87010
11467   -1.015126358 -8.569125 6.538873 -12.56797 10.53772
11468   -0.884912065 -8.438911 6.669087 -12.43776 10.66793
11469   -0.657528361 -8.211527 6.896471 -12.21037 10.89532
11470   -0.425481998 -7.979481 7.128517 -11.97833 11.12736
11471    0.219964978 -7.334034 7.773964 -11.33288 11.77281
11472    0.226407418 -7.327592 7.780406 -11.32644 11.77925

temporary2=copy(MatrixA)

temporary2[,predicted_differ:=differ] 

test2=MatrixA[11425:11448]
test2[,production:=NA]
test2[,predicted_differ:=as.numeric(forecasted2$mean)]

temporary2[11425:11448]=test2


temporary2[,forecastval:=predicted_differ+shift(production,24)]
temporary2[11400:11450,]

A data.table: 51 × 42

date	hour	CLOUD_LOW_LAYER_36.25_33	CLOUD_LOW_LAYER_36.25_33.25	CLOUD_LOW_LAYER_36.25_33.5	CLOUD_LOW_LAYER_36.5_33	CLOUD_LOW_LAYER_36.5_33.25	CLOUD_LOW_LAYER_36.5_33.5	CLOUD_LOW_LAYER_36.75_33	CLOUD_LOW_LAYER_36.75_33.25	⋯	TEMP_36.5_33	TEMP_36.5_33.25	TEMP_36.5_33.5	TEMP_36.75_33	TEMP_36.75_33.25	TEMP_36.75_33.5	production	differ	predicted_differ	forecastval
<dttm>	<int>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	⋯	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>
2022-05-27 23:00:00	23	3.6	0.3	0.0	0.0	1.8	2.3	3.4	4.1	⋯	290.951	293.551	296.651	289.651	294.351	292.751	0.00	0.00	0.000000000	0.000000000
2022-05-28 00:00:00	0	4.0	0.3	0.0	0.6	1.2	1.6	2.2	3.7	⋯	290.396	293.396	295.796	289.396	293.596	291.896	0.00	0.00	0.000000000	0.000000000
2022-05-28 01:00:00	1	3.7	0.6	0.0	0.4	0.9	1.1	1.7	2.8	⋯	289.702	292.802	295.302	288.902	293.202	291.602	0.00	0.00	0.000000000	0.000000000
2022-05-28 02:00:00	2	3.4	0.5	0.0	0.4	1.7	0.9	1.4	2.2	⋯	289.317	292.517	294.917	288.617	293.017	291.417	0.00	0.00	0.000000000	0.000000000
2022-05-28 03:00:00	3	3.3	0.4	0.0	0.4	1.4	0.8	1.2	1.9	⋯	289.051	292.251	294.551	288.351	292.751	291.051	0.00	0.00	0.000000000	0.000000000
2022-05-28 04:00:00	4	0.0	0.0	0.0	0.0	3.4	0.0	0.0	0.0	⋯	288.568	291.968	293.968	287.868	292.168	290.568	0.00	0.00	0.000000000	0.000000000
2022-05-28 05:00:00	5	0.0	0.0	0.0	0.0	1.7	0.0	0.0	0.0	⋯	288.282	291.582	293.482	287.682	291.782	290.282	0.15	-0.06	-0.060000000	0.150000000
2022-05-28 06:00:00	6	0.0	0.0	0.0	0.0	1.2	0.0	0.0	0.3	⋯	288.366	291.666	293.866	287.566	291.766	290.166	6.99	0.19	0.190000000	6.990000000
2022-05-28 07:00:00	7	0.0	0.0	0.0	0.0	0.8	0.0	0.0	1.1	⋯	290.111	293.411	296.711	289.011	293.411	291.811	26.05	0.60	0.600000000	26.050000000
2022-05-28 08:00:00	8	0.0	0.0	0.0	0.0	0.7	0.0	0.1	1.5	⋯	291.800	295.300	298.500	290.900	295.700	294.200	35.00	0.00	0.000000000	35.000000000
2022-05-28 09:00:00	9	0.0	0.0	0.0	0.0	0.5	0.0	0.1	1.2	⋯	293.511	297.011	299.911	292.011	297.311	295.711	35.00	0.00	0.000000000	35.000000000
2022-05-28 10:00:00	10	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	⋯	295.337	298.437	301.637	293.137	298.737	297.037	35.00	0.00	0.000000000	35.000000000
2022-05-28 11:00:00	11	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	⋯	296.250	299.550	303.350	294.050	299.650	297.950	35.00	0.00	0.000000000	35.000000000
2022-05-28 12:00:00	12	0.6	0.0	0.0	0.0	0.0	0.0	0.0	0.0	⋯	297.206	300.406	304.606	294.906	300.406	298.606	35.00	0.00	0.000000000	35.000000000
2022-05-28 13:00:00	13	1.1	0.3	0.0	0.4	0.0	0.0	0.0	0.3	⋯	298.100	301.300	305.500	295.900	301.200	299.400	35.00	0.00	0.000000000	35.000000000
2022-05-28 14:00:00	14	0.9	0.5	0.0	1.3	0.1	0.0	0.0	0.4	⋯	298.700	301.900	306.000	296.500	301.900	299.800	35.00	0.00	0.000000000	35.000000000
2022-05-28 15:00:00	15	8.9	3.5	0.0	1.4	0.1	0.6	0.0	0.5	⋯	297.095	301.495	306.295	297.095	302.495	300.095	32.60	0.12	0.120000000	32.600000000
2022-05-28 16:00:00	16	26.1	18.9	1.5	3.0	1.6	0.0	30.9	4.3	⋯	297.730	300.830	305.430	296.030	301.630	299.830	26.20	22.11	22.110000000	26.200000000
2022-05-28 17:00:00	17	13.1	9.6	0.8	11.7	5.5	0.0	28.8	4.1	⋯	297.632	300.532	305.132	295.432	301.832	298.332	20.97	18.68	18.680000000	20.970000000
2022-05-28 18:00:00	18	9.6	6.8	0.5	26.1	3.8	1.5	26.9	3.2	⋯	296.923	300.623	304.623	294.723	301.123	298.323	9.47	7.33	7.330000000	9.470000000
2022-05-28 19:00:00	19	8.4	5.4	0.5	29.7	4.0	2.1	21.5	3.5	⋯	296.381	300.281	303.181	294.581	300.481	297.381	1.23	0.16	0.160000000	1.230000000
2022-05-28 20:00:00	20	7.7	4.6	0.4	24.2	3.2	1.7	17.2	3.1	⋯	293.800	297.200	300.100	293.100	297.800	295.100	0.00	0.00	0.000000000	0.000000000
2022-05-28 21:00:00	21	6.7	4.0	0.4	20.2	3.3	1.4	14.3	2.7	⋯	292.728	295.828	298.828	291.828	296.028	294.628	0.00	0.00	0.000000000	0.000000000
2022-05-28 22:00:00	22	0.0	0.0	0.0	2.8	0.0	0.0	0.0	0.7	⋯	292.215	295.015	297.615	290.515	295.315	293.815	0.00	0.00	0.000000000	0.000000000
2022-05-28 23:00:00	23	0.9	0.0	0.0	1.4	0.0	0.0	0.0	0.4	⋯	291.642	294.442	297.042	290.042	295.542	293.542	0.00	0.00	0.000000000	0.000000000
2022-05-29 00:00:00	0	0.6	0.0	0.0	1.0	0.0	0.0	0.1	0.3	⋯	291.283	294.383	296.683	289.983	295.283	293.183	NA	NA	0.039614943	0.039614943
2022-05-29 01:00:00	1	0.4	0.0	0.0	0.7	0.0	0.0	0.1	0.2	⋯	290.897	294.197	296.097	289.597	294.897	292.897	NA	NA	0.014967161	0.014967161
2022-05-29 02:00:00	2	0.4	0.0	0.0	0.6	0.0	0.0	0.1	0.2	⋯	290.411	293.911	295.611	289.411	294.311	292.611	NA	NA	-0.004232844	-0.004232844
2022-05-29 03:00:00	3	0.3	0.0	0.0	0.4	0.0	0.0	0.1	0.2	⋯	290.218	293.518	295.118	289.518	293.918	292.318	NA	NA	-0.034728588	-0.034728588
2022-05-29 04:00:00	4	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	⋯	289.841	293.141	294.741	289.141	293.641	292.041	NA	NA	-0.028218354	-0.028218354
2022-05-29 05:00:00	5	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	⋯	289.541	292.841	294.341	288.941	293.141	291.741	NA	NA	-0.015122822	0.134877178
2022-05-29 06:00:00	6	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	⋯	289.859	293.159	294.959	289.059	293.359	291.859	NA	NA	0.006461136	6.996461136
2022-05-29 07:00:00	7	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	⋯	292.959	295.659	298.759	291.359	296.259	294.359	NA	NA	0.177552236	26.227552236
2022-05-29 08:00:00	8	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	⋯	294.500	297.300	300.300	293.300	298.000	296.200	NA	NA	0.166708669	35.166708669
2022-05-29 09:00:00	9	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	⋯	296.014	298.714	301.714	294.614	299.314	297.414	NA	NA	0.179643053	35.179643053
2022-05-29 10:00:00	10	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	⋯	297.406	300.206	303.306	295.706	300.406	298.406	NA	NA	0.403426324	35.403426324
2022-05-29 11:00:00	11	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	⋯	298.488	301.488	304.988	296.588	301.488	299.388	NA	NA	0.430650144	35.430650144
2022-05-29 12:00:00	12	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	⋯	299.524	302.524	306.224	297.524	302.424	300.224	NA	NA	0.456701014	35.456701014
2022-05-29 13:00:00	13	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	⋯	300.357	303.357	306.957	298.357	303.357	301.157	NA	NA	0.468783006	35.468783006
2022-05-29 14:00:00	14	0.0	0.7	0.0	0.0	0.0	0.0	0.0	0.0	⋯	301.157	303.957	307.757	299.057	303.957	301.757	NA	NA	0.421002362	35.421002362
2022-05-29 15:00:00	15	0.0	0.5	0.0	0.0	0.0	0.0	0.0	0.0	⋯	301.236	303.636	307.236	299.236	304.436	302.236	NA	NA	0.202609089	32.802609089
2022-05-29 16:00:00	16	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	⋯	300.539	303.139	306.439	298.739	304.739	301.439	NA	NA	-0.910363105	25.289636895
2022-05-29 17:00:00	17	0.0	0.0	0.0	0.0	0.0	0.0	2.2	0.5	⋯	299.694	302.494	305.594	297.094	303.494	299.994	NA	NA	-0.682742338	20.287257662
2022-05-29 18:00:00	18	0.0	0.0	0.0	1.1	0.1	0.0	3.1	0.7	⋯	298.394	301.294	304.794	296.794	302.094	298.994	NA	NA	-1.015126358	8.454873642
2022-05-29 19:00:00	19	0.0	0.0	0.0	1.6	0.1	0.0	2.9	0.5	⋯	297.702	299.502	303.702	296.102	300.802	297.902	NA	NA	-0.884912065	0.345087935
2022-05-29 20:00:00	20	0.0	0.0	0.0	1.3	0.1	0.0	2.4	0.4	⋯	294.800	297.400	300.600	293.100	298.600	295.800	NA	NA	-0.657528361	-0.657528361
2022-05-29 21:00:00	21	0.0	0.0	0.0	1.1	0.0	0.0	2.0	0.4	⋯	293.729	296.529	299.329	292.029	297.329	295.229	NA	NA	-0.425481998	-0.425481998
2022-05-29 22:00:00	22	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	⋯	293.085	296.385	298.585	291.585	296.685	294.785	NA	NA	0.219964978	0.219964978
2022-05-29 23:00:00	23	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	⋯	292.407	295.707	297.707	291.207	296.007	294.107	NA	NA	0.226407418	0.226407418
NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	⋯	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	⋯	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA

ARIMA with all DSWRF variables and some REL_HUMIDITY variables

#ARIMA with some variables
fitted
nahead=24
reg_matrix3=cbind(MatrixA$REL_HUMIDITY_36.25_33.25,MatrixA$REL_HUMIDITY_36.25_33.5,MatrixA$REL_HUMIDITY_36.5_33.25,MatrixA$REL_HUMIDITY_36.75_33.5,MatrixA$DSWRF_36.25_33,MatrixA$DSWRF_36.25_33.25,MatrixA$DSWRF_36.25_33.5,MatrixA$DSWRF_36.5_33,MatrixA$DSWRF_36.5_33.25,MatrixA$DSWRF_36.5_33.5,MatrixA$DSWRF_36.75_33,MatrixA$DSWRF_36.75_33.25,MatrixA$DSWRF_36.75_33.5) 
fitted_arimax3=auto.arima(MatrixA$differ,xreg=reg_matrix3,seasonal=F,trace=T,stepwise=F,approximation=F)

forecasted3=forecast(fitted_arimax3,xreg=tail(reg_matrix3,24),  h=24)
forecasted3

Series: MatrixA$differ 
ARIMA(1,0,1) with zero mean 

Coefficients:
         ar1     ma1
      0.6822  0.1712
s.e.  0.0090  0.0122

sigma^2 = 15.25:  log likelihood = -31705.54
AIC=63417.08   AICc=63417.09   BIC=63439.11

 ARIMA(0,0,0) with zero mean     : 73005.56
 ARIMA(0,0,0) with non-zero mean : 73000.37
 ARIMA(0,0,1) with zero mean     : 66357.07
 ARIMA(0,0,1) with non-zero mean : 66351.06
 ARIMA(0,0,2) with zero mean     : 64491.03
 ARIMA(0,0,2) with non-zero mean : 64485.17
 ARIMA(0,0,3) with zero mean     : 63806.74
 ARIMA(0,0,3) with non-zero mean : 63801.58
 ARIMA(0,0,4) with zero mean     : 63608.24
 ARIMA(0,0,4) with non-zero mean : 63603.97
 ARIMA(0,0,5) with zero mean     : 63515.11
 ARIMA(0,0,5) with non-zero mean : 63511.56
 ARIMA(1,0,0) with zero mean     : 63581.13
 ARIMA(1,0,0) with non-zero mean : 63578.47
 ARIMA(1,0,1) with zero mean     : 63395.86
 ARIMA(1,0,1) with non-zero mean : 63392.77
 ARIMA(1,0,2) with zero mean     : 63396.5
 ARIMA(1,0,2) with non-zero mean : 63393.44
 ARIMA(1,0,3) with zero mean     : 63398.14
 ARIMA(1,0,3) with non-zero mean : 63395.09
 ARIMA(1,0,4) with zero mean     : 63397.5
 ARIMA(1,0,4) with non-zero mean : 63394.37
 ARIMA(2,0,0) with zero mean     : 63406.88
 ARIMA(2,0,0) with non-zero mean : 63403.76
 ARIMA(2,0,1) with zero mean     : 63396.59
 ARIMA(2,0,1) with non-zero mean : 63393.57
 ARIMA(2,0,2) with zero mean     : 63398.55
 ARIMA(2,0,2) with non-zero mean : 63395.52
 ARIMA(2,0,3) with zero mean     : Inf
 ARIMA(2,0,3) with non-zero mean : Inf
 ARIMA(3,0,0) with zero mean     : 63395.86
 ARIMA(3,0,0) with non-zero mean : 63392.8
 ARIMA(3,0,1) with zero mean     : 63397.63
 ARIMA(3,0,1) with non-zero mean : 63394.64
 ARIMA(3,0,2) with zero mean     : Inf
 ARIMA(3,0,2) with non-zero mean : Inf
 ARIMA(4,0,0) with zero mean     : 63397.72
 ARIMA(4,0,0) with non-zero mean : 63394.64
 ARIMA(4,0,1) with zero mean     : 63399.55
 ARIMA(4,0,1) with non-zero mean : 63396.5
 ARIMA(5,0,0) with zero mean     : 63398.19
 ARIMA(5,0,0) with non-zero mean : 63395.05



 Best model: Regression with ARIMA(1,0,1) errors 

      Point Forecast     Lo 80    Hi 80     Lo 95    Hi 95
11449     0.15388243 -7.490197 7.797962 -11.53673 11.84449
11450     0.18072046 -7.463359 7.824800 -11.50989 11.87133
11451     0.19519414 -7.448885 7.839273 -11.49542 11.88580
11452     0.16281373 -7.481266 7.806893 -11.52780 11.85342
11453     0.08910545 -7.554974 7.733185 -11.60150 11.77972
11454     0.08674720 -7.557332 7.730826 -11.60386 11.77736
11455     0.05812610 -7.585953 7.702205 -11.63248 11.74874
11456     0.18325337 -7.460826 7.827333 -11.50736 11.87386
11457     0.31703899 -7.327040 7.961118 -11.37357 12.00765
11458     0.38038822 -7.263691 8.024467 -11.31022 12.07100
11459     0.57001518 -7.074064 8.214094 -11.12060 12.26063
11460     0.57397535 -7.070104 8.218055 -11.11664 12.26459
11461     0.56632777 -7.077751 8.210407 -11.12428 12.25694
11462     0.62055098 -7.023528 8.264630 -11.07006 12.31116
11463     0.62396133 -7.020118 8.268041 -11.06665 12.31457
11464     0.54723105 -7.096848 8.191310 -11.14338 12.23784
11465    -0.14265297 -7.786732 7.501426 -11.83326 11.54796
11466     0.09047757 -7.553602 7.734557 -11.60013 11.78109
11467    -0.27303186 -7.917111 7.371047 -11.96364 11.41758
11468    -0.46060764 -8.104687 7.183472 -12.15122 11.23000
11469    -0.57332944 -8.217409 7.070750 -12.26394 11.11728
11470    -0.43385866 -8.077938 7.210221 -12.12447 11.25675
11471     0.07357205 -7.570507 7.717651 -11.61704 11.76418
11472     0.12873935 -7.515340 7.772819 -11.56187 11.81935

temporary3=copy(MatrixA)

temporary3[,predicted_differ:=differ] 

test3=MatrixA[11425:11448]
test3[,production:=NA]
test3[,predicted_differ:=as.numeric(forecasted3$mean)]

temporary3[11425:11448]=test3


temporary3[,forecastval:=predicted_differ+shift(production,24)]
temporary3[11400:11450,]

A data.table: 51 × 42

date	hour	CLOUD_LOW_LAYER_36.25_33	CLOUD_LOW_LAYER_36.25_33.25	CLOUD_LOW_LAYER_36.25_33.5	CLOUD_LOW_LAYER_36.5_33	CLOUD_LOW_LAYER_36.5_33.25	CLOUD_LOW_LAYER_36.5_33.5	CLOUD_LOW_LAYER_36.75_33	CLOUD_LOW_LAYER_36.75_33.25	⋯	TEMP_36.5_33	TEMP_36.5_33.25	TEMP_36.5_33.5	TEMP_36.75_33	TEMP_36.75_33.25	TEMP_36.75_33.5	production	differ	predicted_differ	forecastval
<dttm>	<int>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	⋯	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>
2022-05-27 23:00:00	23	3.6	0.3	0.0	0.0	1.8	2.3	3.4	4.1	⋯	290.951	293.551	296.651	289.651	294.351	292.751	0.00	0.00	0.00000000	0.00000000
2022-05-28 00:00:00	0	4.0	0.3	0.0	0.6	1.2	1.6	2.2	3.7	⋯	290.396	293.396	295.796	289.396	293.596	291.896	0.00	0.00	0.00000000	0.00000000
2022-05-28 01:00:00	1	3.7	0.6	0.0	0.4	0.9	1.1	1.7	2.8	⋯	289.702	292.802	295.302	288.902	293.202	291.602	0.00	0.00	0.00000000	0.00000000
2022-05-28 02:00:00	2	3.4	0.5	0.0	0.4	1.7	0.9	1.4	2.2	⋯	289.317	292.517	294.917	288.617	293.017	291.417	0.00	0.00	0.00000000	0.00000000
2022-05-28 03:00:00	3	3.3	0.4	0.0	0.4	1.4	0.8	1.2	1.9	⋯	289.051	292.251	294.551	288.351	292.751	291.051	0.00	0.00	0.00000000	0.00000000
2022-05-28 04:00:00	4	0.0	0.0	0.0	0.0	3.4	0.0	0.0	0.0	⋯	288.568	291.968	293.968	287.868	292.168	290.568	0.00	0.00	0.00000000	0.00000000
2022-05-28 05:00:00	5	0.0	0.0	0.0	0.0	1.7	0.0	0.0	0.0	⋯	288.282	291.582	293.482	287.682	291.782	290.282	0.15	-0.06	-0.06000000	0.15000000
2022-05-28 06:00:00	6	0.0	0.0	0.0	0.0	1.2	0.0	0.0	0.3	⋯	288.366	291.666	293.866	287.566	291.766	290.166	6.99	0.19	0.19000000	6.99000000
2022-05-28 07:00:00	7	0.0	0.0	0.0	0.0	0.8	0.0	0.0	1.1	⋯	290.111	293.411	296.711	289.011	293.411	291.811	26.05	0.60	0.60000000	26.05000000
2022-05-28 08:00:00	8	0.0	0.0	0.0	0.0	0.7	0.0	0.1	1.5	⋯	291.800	295.300	298.500	290.900	295.700	294.200	35.00	0.00	0.00000000	35.00000000
2022-05-28 09:00:00	9	0.0	0.0	0.0	0.0	0.5	0.0	0.1	1.2	⋯	293.511	297.011	299.911	292.011	297.311	295.711	35.00	0.00	0.00000000	35.00000000
2022-05-28 10:00:00	10	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	⋯	295.337	298.437	301.637	293.137	298.737	297.037	35.00	0.00	0.00000000	35.00000000
2022-05-28 11:00:00	11	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	⋯	296.250	299.550	303.350	294.050	299.650	297.950	35.00	0.00	0.00000000	35.00000000
2022-05-28 12:00:00	12	0.6	0.0	0.0	0.0	0.0	0.0	0.0	0.0	⋯	297.206	300.406	304.606	294.906	300.406	298.606	35.00	0.00	0.00000000	35.00000000
2022-05-28 13:00:00	13	1.1	0.3	0.0	0.4	0.0	0.0	0.0	0.3	⋯	298.100	301.300	305.500	295.900	301.200	299.400	35.00	0.00	0.00000000	35.00000000
2022-05-28 14:00:00	14	0.9	0.5	0.0	1.3	0.1	0.0	0.0	0.4	⋯	298.700	301.900	306.000	296.500	301.900	299.800	35.00	0.00	0.00000000	35.00000000
2022-05-28 15:00:00	15	8.9	3.5	0.0	1.4	0.1	0.6	0.0	0.5	⋯	297.095	301.495	306.295	297.095	302.495	300.095	32.60	0.12	0.12000000	32.60000000
2022-05-28 16:00:00	16	26.1	18.9	1.5	3.0	1.6	0.0	30.9	4.3	⋯	297.730	300.830	305.430	296.030	301.630	299.830	26.20	22.11	22.11000000	26.20000000
2022-05-28 17:00:00	17	13.1	9.6	0.8	11.7	5.5	0.0	28.8	4.1	⋯	297.632	300.532	305.132	295.432	301.832	298.332	20.97	18.68	18.68000000	20.97000000
2022-05-28 18:00:00	18	9.6	6.8	0.5	26.1	3.8	1.5	26.9	3.2	⋯	296.923	300.623	304.623	294.723	301.123	298.323	9.47	7.33	7.33000000	9.47000000
2022-05-28 19:00:00	19	8.4	5.4	0.5	29.7	4.0	2.1	21.5	3.5	⋯	296.381	300.281	303.181	294.581	300.481	297.381	1.23	0.16	0.16000000	1.23000000
2022-05-28 20:00:00	20	7.7	4.6	0.4	24.2	3.2	1.7	17.2	3.1	⋯	293.800	297.200	300.100	293.100	297.800	295.100	0.00	0.00	0.00000000	0.00000000
2022-05-28 21:00:00	21	6.7	4.0	0.4	20.2	3.3	1.4	14.3	2.7	⋯	292.728	295.828	298.828	291.828	296.028	294.628	0.00	0.00	0.00000000	0.00000000
2022-05-28 22:00:00	22	0.0	0.0	0.0	2.8	0.0	0.0	0.0	0.7	⋯	292.215	295.015	297.615	290.515	295.315	293.815	0.00	0.00	0.00000000	0.00000000
2022-05-28 23:00:00	23	0.9	0.0	0.0	1.4	0.0	0.0	0.0	0.4	⋯	291.642	294.442	297.042	290.042	295.542	293.542	0.00	0.00	0.00000000	0.00000000
2022-05-29 00:00:00	0	0.6	0.0	0.0	1.0	0.0	0.0	0.1	0.3	⋯	291.283	294.383	296.683	289.983	295.283	293.183	NA	NA	0.15388243	0.15388243
2022-05-29 01:00:00	1	0.4	0.0	0.0	0.7	0.0	0.0	0.1	0.2	⋯	290.897	294.197	296.097	289.597	294.897	292.897	NA	NA	0.18072046	0.18072046
2022-05-29 02:00:00	2	0.4	0.0	0.0	0.6	0.0	0.0	0.1	0.2	⋯	290.411	293.911	295.611	289.411	294.311	292.611	NA	NA	0.19519414	0.19519414
2022-05-29 03:00:00	3	0.3	0.0	0.0	0.4	0.0	0.0	0.1	0.2	⋯	290.218	293.518	295.118	289.518	293.918	292.318	NA	NA	0.16281373	0.16281373
2022-05-29 04:00:00	4	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	⋯	289.841	293.141	294.741	289.141	293.641	292.041	NA	NA	0.08910545	0.08910545
2022-05-29 05:00:00	5	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	⋯	289.541	292.841	294.341	288.941	293.141	291.741	NA	NA	0.08674720	0.23674720
2022-05-29 06:00:00	6	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	⋯	289.859	293.159	294.959	289.059	293.359	291.859	NA	NA	0.05812610	7.04812610
2022-05-29 07:00:00	7	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	⋯	292.959	295.659	298.759	291.359	296.259	294.359	NA	NA	0.18325337	26.23325337
2022-05-29 08:00:00	8	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	⋯	294.500	297.300	300.300	293.300	298.000	296.200	NA	NA	0.31703899	35.31703899
2022-05-29 09:00:00	9	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	⋯	296.014	298.714	301.714	294.614	299.314	297.414	NA	NA	0.38038822	35.38038822
2022-05-29 10:00:00	10	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	⋯	297.406	300.206	303.306	295.706	300.406	298.406	NA	NA	0.57001518	35.57001518
2022-05-29 11:00:00	11	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	⋯	298.488	301.488	304.988	296.588	301.488	299.388	NA	NA	0.57397535	35.57397535
2022-05-29 12:00:00	12	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	⋯	299.524	302.524	306.224	297.524	302.424	300.224	NA	NA	0.56632777	35.56632777
2022-05-29 13:00:00	13	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	⋯	300.357	303.357	306.957	298.357	303.357	301.157	NA	NA	0.62055098	35.62055098
2022-05-29 14:00:00	14	0.0	0.7	0.0	0.0	0.0	0.0	0.0	0.0	⋯	301.157	303.957	307.757	299.057	303.957	301.757	NA	NA	0.62396133	35.62396133
2022-05-29 15:00:00	15	0.0	0.5	0.0	0.0	0.0	0.0	0.0	0.0	⋯	301.236	303.636	307.236	299.236	304.436	302.236	NA	NA	0.54723105	33.14723105
2022-05-29 16:00:00	16	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	⋯	300.539	303.139	306.439	298.739	304.739	301.439	NA	NA	-0.14265297	26.05734703
2022-05-29 17:00:00	17	0.0	0.0	0.0	0.0	0.0	0.0	2.2	0.5	⋯	299.694	302.494	305.594	297.094	303.494	299.994	NA	NA	0.09047757	21.06047757
2022-05-29 18:00:00	18	0.0	0.0	0.0	1.1	0.1	0.0	3.1	0.7	⋯	298.394	301.294	304.794	296.794	302.094	298.994	NA	NA	-0.27303186	9.19696814
2022-05-29 19:00:00	19	0.0	0.0	0.0	1.6	0.1	0.0	2.9	0.5	⋯	297.702	299.502	303.702	296.102	300.802	297.902	NA	NA	-0.46060764	0.76939236
2022-05-29 20:00:00	20	0.0	0.0	0.0	1.3	0.1	0.0	2.4	0.4	⋯	294.800	297.400	300.600	293.100	298.600	295.800	NA	NA	-0.57332944	-0.57332944
2022-05-29 21:00:00	21	0.0	0.0	0.0	1.1	0.0	0.0	2.0	0.4	⋯	293.729	296.529	299.329	292.029	297.329	295.229	NA	NA	-0.43385866	-0.43385866
2022-05-29 22:00:00	22	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	⋯	293.085	296.385	298.585	291.585	296.685	294.785	NA	NA	0.07357205	0.07357205
2022-05-29 23:00:00	23	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	⋯	292.407	295.707	297.707	291.207	296.007	294.107	NA	NA	0.12873935	0.12873935
NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	⋯	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	⋯	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA