Temperature Climate Forecasting
By : Bayu Raka Janasri
6/2/2021
1 Introduction
Hello everyone !!!
The Dataset is Indian climate, this dataset provides data from 1st January 2013 to 24th April 2017 in the city of Delhi, India. The 4 parameters here are meantemp, humidity, wind_speed, meanpressure. At this moment we will build some models for predict temperature using this dataset.
Source: https://www.kaggle.com/sumanthvrao/daily-climate-time-series-data.
2 Data Preparation
2.1 Import Library
library(dplyr) # for data wrangling
library(lubridate) # date manipulation
library(TSstudio) # time series interactive viz
library(forecast) # time series library
library(tseries) # for adf.test2.2 Read Data
From the dataset there are already train and data test, we don’t have to split them into two data anymore.
2.2.1 Import data train
climate_train <- read.csv("DailyDelhiClimateTrain.csv")
head(climate_train)2.2.2 Import data test
climate_test <- read.csv("DailyDelhiClimateTest.csv")
head(climate_test)2.3 Check data type
glimpse(climate_train)## Rows: 1,462
## Columns: 5
## $ date <chr> "2013-01-01", "2013-01-02", "2013-01-03", "2013-01-04", "…
## $ meantemp <dbl> 10.000000, 7.400000, 7.166667, 8.666667, 6.000000, 7.0000…
## $ humidity <dbl> 84.50000, 92.00000, 87.00000, 71.33333, 86.83333, 82.8000…
## $ wind_speed <dbl> 0.0000000, 2.9800000, 4.6333333, 1.2333333, 3.7000000, 1.…
## $ meanpressure <dbl> 1015.667, 1017.800, 1018.667, 1017.167, 1016.500, 1018.00…Time series is a method of analyzing and processing data in which the values are affected by time. The action of predicting future values based on its value in the previous period of time is called forecasting.
The data which formatted into a time series (ts) object must have some characteristics:
- no missing intervals
- no missing values
- data should be ordered by time
2.4 Check Missing Value
We have to check if there is any missing values in our dataset. There is no missing value on our dataset.
anyNA(climate_train)## [1] FALSEanyNA(climate_test)## [1] FALSE2.5 Check data range
We have to check our data range. This is important for time series prediction, it can help us for choosing right frequency.
range(climate_train$date)## [1] "2013-01-01" "2017-01-01"range(climate_test$date)## [1] "2017-01-01" "2017-04-24"2.6 Check missing interval
interval(start = head(climate_train$date)[1], end = tail(climate_train$date)[1])## [1] 2013-01-01 UTC--2016-12-27 UTCinterval(start = head(climate_test$date)[1], end = tail(climate_test$date)[1])## [1] 2017-01-01 UTC--2017-04-19 UTC3 Data Pre-processing
3.1 Feature Engineering
3.1.1 Selecting column
Take date and meantemp column form test data.
test_clean <- climate_test %>%
select(date, meantemp)Take date and meantemp column for train data.
train_clean <- climate_train %>%
select(date, meantemp)3.1.2 Create time series object for data train
After creating ts object, we can plot our object and see the graph.
ts_train <- ts(data = train_clean$meantemp,
start = c(2013,01),
frequency = 365)
autoplot(ts_train)
### Create time series object for data test
After creating ts object, we can plot our object and see the graph.
ts_test <- ts(data = test_clean$meantemp,
start = c(2017,01),
frequency = 365)
autoplot(ts_test)
### Decompose
Decomposing a time series means separating it into its constituent components.
climate_dc <- decompose(ts_train)
plot(climate_dc)
From our graph above we conclude our dataset have trend and seasonal. This is important to know what is our data characteristic, we choose their model based on their character.
4 Modeling
4.1 Holt-Winters Model
4.1.1 Create Holt-Winters Model
climate_hw <- HoltWinters(ts_train,seasonal = "additive")
climate_hw## Holt-Winters exponential smoothing with trend and additive seasonal component.
##
## Call:
## HoltWinters(x = ts_train, seasonal = "additive")
##
## Smoothing parameters:
## alpha: 0.7137593
## beta : 0
## gamma: 1
##
## Coefficients:
## [,1]
## a 23.2059477677
## b 0.0007786026
## s1 -11.9533349288
## s2 -11.5762825721
## s3 -11.9041600160
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## s365 -13.20594776774.1.2 Forecast model
climate_forecast <- forecast(climate_hw, h=114)
climate_forecast## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## 2017.0055 11.253391 8.8448898 13.66189 7.56990607 14.93688
## 2017.0082 11.631222 8.6721429 14.59030 7.10570078 16.15674
## 2017.0110 11.304124 7.8819279 14.72632 6.07032691 16.53792
## 2017.0137 10.741664 6.9119515 14.57138 4.88462432 16.59870
## 2017.0164 10.095896 5.8980430 14.29375 3.67583403 16.51596
## 2017.0192 9.942621 5.4064073 14.47884 3.00508059 16.88016
## 2017.0219 11.118681 6.2676490 15.96971 3.69966787 18.53769
## 2017.0247 11.208151 6.0615232 16.35478 3.33706280 19.07924
## 2017.0274 11.049992 5.6238466 16.47614 2.75141882 19.34857
## 2017.0301 11.860111 6.1681586 17.55206 3.15502087 20.56520
## 2017.0329 12.574862 6.6289731 18.52075 3.48140963 21.66831
## 2017.0356 12.290857 6.1014411 18.48027 2.82496228 21.75675
## 2017.0384 11.013761 4.5900444 17.43748 1.18953406 20.83799
## 2017.0411 11.396001 4.7462329 18.04577 1.22605851 21.56594
## 2017.0438 11.236718 4.3683347 18.10510 0.73243248 21.74100
## 2017.0466 10.858868 3.7786166 17.93912 0.03055815 21.68718
## 2017.0493 11.969222 4.6832612 19.25518 0.82630651 23.11214
## 2017.0521 12.656793 5.1707729 20.14281 1.20791326 24.10567
## 2017.0548 12.537658 4.8567880 20.21853 0.79078082 24.28454
## 2017.0575 12.968446 5.0975481 20.83934 0.93094620 25.00595
## 2017.0603 14.903008 6.8465631 22.95945 2.58173851 27.22428
## 2017.0630 12.250051 4.0122367 20.48787 -0.34859877 24.84870
## 2017.0658 11.681094 3.2658187 20.09637 -1.18895890 24.55115
## 2017.0685 13.217548 4.6284780 21.80662 0.08169883 26.35340
## 2017.0712 14.925451 6.1660334 23.68487 1.52907774 28.32182
## 2017.0740 14.484502 5.5579866 23.41102 0.83257496 28.13643
## 2017.0767 14.759192 5.6686508 23.84973 0.85640887 28.66198
## 2017.0795 14.167724 4.9160636 23.41938 0.01853058 28.31692
## 2017.0822 13.094642 3.6846213 22.50466 -1.29674265 27.48603
## 2017.0849 12.827346 3.2615861 22.39311 -1.80222116 27.45691
## 2017.0877 13.800582 4.0815784 23.51959 -1.06335123 28.66452
## 2017.0904 14.863798 4.9939294 24.73367 -0.23086328 29.95846
## 2017.0932 16.973466 6.9550040 26.99193 1.65155079 32.29538
## 2017.0959 15.151617 4.9867340 25.31650 -0.39422998 30.69746
## 2017.0986 17.188190 6.8789650 27.49741 1.42159109 32.95479
## 2017.1014 17.923080 7.4715064 28.37465 1.93877768 33.90738
## 2017.1041 15.648207 5.0561978 26.24022 -0.55087312 31.84729
## 2017.1068 13.480211 2.7496038 24.21082 -2.93083655 29.89126
## 2017.1096 11.991050 1.1236128 22.85849 -4.62926120 28.61136
## 2017.1123 12.343031 1.3404640 23.34560 -4.48394300 29.17000
## 2017.1151 11.765906 0.6298501 22.90196 -5.26522190 28.79703
## 2017.1178 12.580505 1.3125406 23.84847 -4.65235932 29.81337
## 2017.1205 12.931522 1.5331761 24.32987 -4.50074367 30.36379
## 2017.1233 11.807318 0.2800654 23.33457 -5.82209364 29.43673
## 2017.1260 12.401682 0.7469482 24.05642 -5.42269548 30.22606
## 2017.1288 13.318966 1.5381298 25.09980 -4.69826820 31.33620
## 2017.1315 13.850905 1.9453027 25.75651 -4.35714264 32.05895
## 2017.1342 15.113295 3.0842198 27.14237 -3.28358787 33.51018
## 2017.1370 14.828438 2.6771453 26.97973 -3.75536061 33.41224
## 2017.1397 14.264633 1.9923396 26.53693 -4.50422021 33.03349
## 2017.1425 14.945985 2.5538725 27.33810 -4.00611575 33.89809
## 2017.1452 15.038383 2.5275984 27.54917 -4.09521091 34.17198
## 2017.1479 15.295298 2.6669565 27.92364 -4.01808355 34.60868
## 2017.1507 16.283464 3.5386498 29.02828 -3.20804700 35.77497
## 2017.1534 16.221672 3.3614405 29.08190 -3.44635473 35.88970
## 2017.1562 16.511253 3.5366311 29.48588 -3.33171893 36.35423
## 2017.1589 15.793730 2.7057165 28.88174 -4.22265917 35.81012
## 2017.1616 14.600815 1.4003844 27.80125 -5.58750138 34.78913
## 2017.1644 14.779221 1.4673226 28.09112 -5.57957068 35.13801
## 2017.1671 15.284089 1.8616483 28.70653 -5.24376245 35.81194
## 2017.1699 16.749630 3.2175508 30.28171 -3.94589941 37.44516
## 2017.1726 17.907073 4.2662356 31.54791 -2.95478759 38.76893
## 2017.1753 16.684201 2.9354654 30.43294 -4.34267542 37.71108
## 2017.1781 16.403470 2.5476774 30.25926 -4.78713616 37.59408
## 2017.1808 18.003578 4.0415485 31.96561 -3.34950336 39.35666
## 2017.1836 19.010164 4.9427004 33.07763 -2.50416508 40.52449
## 2017.1863 18.980797 4.8086838 33.15291 -2.69358004 40.65518
## 2017.1890 19.637181 5.3611841 33.91318 -2.19607196 41.47043
## 2017.1918 19.339683 4.9605541 33.71881 -2.65129699 41.33066
## 2017.1945 18.496337 4.0148098 32.97786 -3.65124747 40.64392
## 2017.1973 18.262965 3.6797592 32.84617 -4.04012367 40.56605
## 2017.2000 17.940468 3.2562873 32.62465 -4.51704848 40.39798
## 2017.2027 20.938416 6.1539495 35.72288 -1.67247410 43.54931
## 2017.2055 23.214650 8.3305747 38.09873 0.45142100 45.97788
## 2017.2082 24.093053 9.1100295 39.07608 1.17849620 47.00761
## 2017.2110 22.211131 7.1298099 37.29245 -0.85375935 45.27602
## 2017.2137 21.447069 6.2680863 36.62605 -1.76718191 44.66132
## 2017.2164 21.745321 6.4693007 37.02134 -1.61733591 45.10798
## 2017.2192 22.591130 7.2186853 37.96358 -0.91899555 46.10126
## 2017.2219 21.539606 6.0713376 37.00788 -2.11706920 45.19628
## 2017.2247 21.813789 6.2502866 37.37729 -1.98853390 45.61611
## 2017.2274 23.182747 7.5245901 38.84090 -0.76433753 47.12983
## 2017.2301 24.283933 8.5316904 40.03618 0.19295681 48.37491
## 2017.2329 21.386869 5.5410994 37.23264 -2.84714454 45.62088
## 2017.2356 22.776158 6.8374098 38.71491 -1.60005390 47.15237
## 2017.2384 23.111717 7.0805296 39.14290 -1.40586840 47.62930
## 2017.2411 22.987565 6.8644681 39.11066 -1.67058360 47.64571
## 2017.2438 23.786378 7.5718938 40.00086 -1.01153582 48.58429
## 2017.2466 23.834700 7.5293393 40.14006 -1.10219716 48.77160
## 2017.2493 25.181530 8.7857976 41.57726 0.10642090 50.25664
## 2017.2521 24.050411 7.5648015 40.53602 -1.16215311 49.26298
## 2017.2548 23.565053 6.9900536 40.14005 -1.78422098 48.91433
## 2017.2575 25.018475 8.3545656 41.68238 -0.46677505 50.50372
## 2017.2603 27.177016 10.4246683 43.92936 1.55651130 52.79752
## 2017.2630 26.154856 9.3145352 42.99518 0.39980774 51.90990
## 2017.2658 25.157177 8.2293398 42.08501 -0.73171614 51.04607
## 2017.2685 24.626770 7.6118656 41.64167 -1.39528045 50.64882
## 2017.2712 25.427219 8.3256921 42.52875 -0.72730950 51.58175
## 2017.2740 26.672678 9.4849647 43.86039 0.38633872 52.95902
## 2017.2767 25.658862 8.3853917 42.93233 -0.75863106 52.07635
## 2017.2795 25.839524 8.4807213 43.19833 -0.70847392 52.38752
## 2017.2822 26.733521 9.2898021 44.17724 0.05565536 53.41139
## 2017.2849 27.764615 10.2363925 45.29284 0.95751195 54.57172
## 2017.2877 26.326777 8.7144563 43.93910 -0.60894331 53.26250
## 2017.2904 26.633076 8.9370563 44.32910 -0.43065085 53.69680
## 2017.2932 24.657690 6.8783646 42.43701 -2.53344156 51.84882
## 2017.2959 24.738707 6.8764659 42.60095 -2.57923359 52.05665
## 2017.2986 25.146979 7.2022042 43.09175 -2.29718574 52.59114
## 2017.3014 25.745508 7.7185774 43.77244 -1.82430303 53.31532
## 2017.3041 26.688301 8.5795882 44.79701 -1.00658544 54.38319
## 2017.3068 27.071620 8.8814920 45.26175 -0.74778014 54.89102
## 2017.3096 27.307823 9.0366428 45.57900 -0.63553581 55.25118
## 2017.3123 28.099498 9.7476229 46.45137 0.03272736 56.16627
## 2017.3151 28.985223 10.5530074 47.41744 0.79558180 57.174864.1.3 Check Accuracy
forecast::accuracy(climate_forecast, ts_test)## ME RMSE MAE MPE MAPE MASE
## Training set -0.002952318 1.878509 1.317623 -0.254612 5.509781 0.5153414
## Test set 3.947982827 4.875027 4.125055 17.527790 18.548411 1.6133681
## ACF1 Theil's U
## Training set 0.1324813 NA
## Test set 0.7569823 2.5280384.2 Arima Model
Before creating arima model, we have to make sure our data is stationary by using adf.test() from library tseries.
4.2.1 Check stationary data
adf.test(ts_train)##
## Augmented Dickey-Fuller Test
##
## data: ts_train
## Dickey-Fuller = -1.8526, Lag order = 11, p-value = 0.6407
## alternative hypothesis: stationaryOur p-value > 0.05 that means our data is not stationer. If our data is not stationer we have to differencing.
ts_train_diff <- ts_train %>% diff()
adf.test(ts_train_diff)## Warning in adf.test(ts_train_diff): p-value smaller than printed p-value##
## Augmented Dickey-Fuller Test
##
## data: ts_train_diff
## Dickey-Fuller = -14.011, Lag order = 11, p-value = 0.01
## alternative hypothesis: stationaryAfter differencing our p-value < 0.05, it means our data already stationer.
4.2.2 Create Arima model
climate_auto <- auto.arima(ts_train, seasonal = T)
climate_auto## Series: ts_train
## ARIMA(3,1,1)(0,1,0)[365]
##
## Coefficients:
## ar1 ar2 ar3 ma1
## 0.7188 0.0102 -0.0375 -0.9883
## s.e. 0.0311 0.0373 0.0311 0.0081
##
## sigma^2 estimated as 4.591: log likelihood=-2392.92
## AIC=4795.84 AICc=4795.9 BIC=4820.844.2.3 Forecast Arima
climate_auto_f <- forecast(climate_auto, h=114)
climate_auto_f## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## 2017.0055 12.12254 9.376510 14.86857 7.922850 16.32223
## 2017.0082 14.66313 11.262423 18.06384 9.462196 19.86407
## 2017.0110 15.76459 12.046968 19.48221 10.078977 21.45020
## 2017.0137 17.98450 14.127026 21.84196 12.085005 23.88399
## 2017.0164 18.18871 14.266076 22.11135 12.189558 24.18787
## 2017.0192 16.85897 12.904832 20.81310 10.811640 22.90629
## 2017.0219 17.40756 13.437174 21.37794 11.335382 23.47973
## 2017.0247 17.29901 13.319572 21.27845 11.212983 23.38504
## 2017.0274 17.50375 13.518768 21.48872 11.409248 23.59824
## 2017.0301 19.80514 15.816442 23.79385 13.704951 25.90534
## 2017.0329 20.10494 16.113490 24.09638 14.000546 26.20933
## 2017.0356 17.42212 13.428477 21.41576 11.314371 23.52986
## 2017.0384 14.87337 10.877862 18.86889 8.762766 20.98398
## 2017.0411 15.48224 11.485049 19.47943 9.369065 21.59541
## 2017.0438 15.88795 11.889204 19.88670 9.772396 22.00350
## 2017.0466 15.15830 11.158070 19.15853 9.040477 21.27612
## 2017.0493 14.25115 10.249483 18.25281 8.131131 20.37116
## 2017.0521 13.96220 9.959131 17.96526 7.840036 20.08436
## 2017.0548 14.08402 10.079565 18.08847 7.959736 20.20830
## 2017.0575 13.63048 9.624661 17.63631 7.504106 19.75686
## 2017.0603 16.33506 12.327873 20.34225 10.206596 22.46352
## 2017.0630 13.08532 9.076778 17.09387 6.954783 19.21586
## 2017.0658 13.56466 9.554760 17.57456 7.432048 19.69727
## 2017.0685 16.46060 12.449351 20.47185 10.325923 22.59528
## 2017.0712 19.48151 15.468905 23.49411 13.344762 25.61825
## 2017.0740 18.75536 14.741411 22.76931 12.616554 24.89417
## 2017.0767 21.46075 17.445450 25.47605 15.319879 27.60162
## 2017.0795 22.04112 18.024479 26.05777 15.898195 28.18405
## 2017.0822 19.27328 15.255287 23.29127 13.128291 25.41827
## 2017.0849 17.74444 13.725103 21.76378 11.597395 23.89149
## 2017.0877 17.16496 13.144276 21.18564 11.015855 23.31406
## 2017.0904 15.02329 11.001268 19.04532 8.872136 21.17445
## 2017.0932 18.26193 14.238562 22.28530 12.108718 24.41515
## 2017.0959 14.56496 10.540250 18.58968 8.409695 20.72023
## 2017.0986 17.23163 13.205575 21.25769 11.074308 23.38896
## 2017.1014 17.52330 13.495899 21.55070 11.363922 23.68268
## 2017.1041 18.98921 14.960466 23.01795 12.827779 25.15064
## 2017.1068 19.66753 15.637446 23.69762 13.504049 25.83101
## 2017.1096 20.03163 16.000208 24.06306 13.866100 26.19717
## 2017.1123 21.58580 17.553034 25.61857 15.418216 27.75339
## 2017.1151 21.09830 17.064193 25.13241 14.928666 27.26794
## 2017.1178 18.96497 14.929520 23.00041 12.793283 25.13665
## 2017.1205 19.54116 15.504371 23.57794 13.367425 25.71489
## 2017.1233 19.49830 15.460174 23.53643 13.322520 25.67408
## 2017.1260 20.11259 16.073121 24.15205 13.934758 26.29041
## 2017.1288 20.61259 16.571783 24.65339 14.432711 26.79246
## 2017.1315 21.36497 17.322826 25.40711 15.183046 27.54689
## 2017.1342 25.05215 21.008668 29.09563 18.868180 31.23611
## 2017.1370 25.52330 21.478485 29.56812 19.337290 31.70931
## 2017.1397 22.89830 18.852149 26.94445 16.710246 29.08636
## 2017.1425 22.89830 18.850813 26.94579 16.708202 29.08840
## 2017.1452 23.32687 19.278049 27.37570 17.134731 29.51901
## 2017.1479 23.58580 19.535642 27.63596 17.391618 29.77998
## 2017.1507 24.46080 20.409307 28.51229 18.264576 30.65702
## 2017.1534 24.69830 20.645473 28.75113 18.500036 30.89657
## 2017.1562 24.69830 20.644139 28.75246 18.497996 30.89861
## 2017.1589 24.89830 20.842806 28.95380 18.695957 31.10064
## 2017.1616 25.77330 21.716473 29.83013 19.568918 31.97768
## 2017.1644 26.81497 22.756807 30.87313 20.608547 33.02139
## 2017.1671 26.83163 22.772142 30.89113 20.623176 33.04009
## 2017.1699 27.89830 23.837477 31.95912 21.687806 34.10880
## 2017.1726 29.21080 25.148645 33.27296 22.998270 35.42333
## 2017.1753 25.83163 21.768148 29.89512 19.617068 32.04620
## 2017.1781 24.71080 20.645984 28.77562 18.494200 30.92740
## 2017.1808 25.61259 21.546440 29.67873 19.393952 31.83122
## 2017.1836 25.32687 21.259396 29.39435 19.106205 31.54754
## 2017.1863 25.89830 21.829496 29.96711 19.675601 32.12100
## 2017.1890 27.46080 23.390667 31.53093 21.236069 33.68553
## 2017.1918 26.96497 22.893506 31.03643 20.738204 33.19173
## 2017.1945 26.46080 22.388011 30.53359 20.232007 32.68959
## 2017.1973 26.14830 22.074184 30.22242 19.917477 32.37912
## 2017.2000 24.27330 20.197857 28.34874 18.040447 30.50615
## 2017.2027 25.96497 21.888197 30.04174 19.730085 32.19985
## 2017.2055 25.83580 21.757705 29.91390 19.598891 32.07271
## 2017.2082 28.21080 24.131379 32.29022 21.971864 34.44974
## 2017.2110 28.08580 24.005054 32.16655 21.844837 34.32676
## 2017.2137 28.68401 24.601943 32.76609 22.441025 34.92700
## 2017.2164 29.03163 24.948238 33.11503 22.786619 35.27665
## 2017.2192 28.52330 24.438581 32.60802 22.276261 34.77034
## 2017.2219 26.96080 22.874757 31.04684 20.711737 33.20986
## 2017.2247 28.09830 24.010934 32.18567 21.847213 34.34939
## 2017.2274 30.03163 25.942945 34.12032 23.778524 36.28474
## 2017.2301 31.77330 27.683290 35.86331 25.518169 38.02843
## 2017.2329 26.56497 22.473635 30.65630 20.307814 32.82212
## 2017.2356 28.14830 24.055647 32.24095 21.889127 34.40747
## 2017.2384 27.83163 23.737659 31.92561 21.570440 34.09283
## 2017.2411 29.02330 24.928005 33.11860 22.760087 35.28651
## 2017.2438 31.46973 27.373114 35.56634 25.204497 37.73496
## 2017.2466 31.89830 27.800366 35.99624 25.631050 38.16555
## 2017.2493 32.46973 28.370475 36.56898 26.200461 38.73900
## 2017.2521 34.21080 30.110228 38.31137 27.939516 40.48209
## 2017.2548 35.21080 31.108909 39.31269 28.937500 41.48410
## 2017.2575 34.71080 30.607592 38.81401 28.435484 40.98612
## 2017.2603 34.21080 30.106274 38.31533 27.933469 40.48813
## 2017.2630 33.27330 29.167457 37.37914 26.993955 39.55265
## 2017.2658 31.83163 27.724474 35.93879 25.550275 38.11299
## 2017.2685 31.16497 27.056491 35.27344 24.881595 37.44834
## 2017.2712 32.63163 28.521842 36.74143 26.346249 38.91702
## 2017.2740 34.14830 30.037193 38.25941 27.860904 40.43570
## 2017.2767 31.69830 27.585878 35.81072 25.408893 37.98771
## 2017.2795 32.09830 27.984564 36.21204 25.806883 38.38972
## 2017.2822 33.64830 29.533249 37.76335 27.354873 39.94173
## 2017.2849 35.02330 30.906936 39.13967 28.727864 41.31874
## 2017.2877 35.52330 31.405623 39.64098 29.225855 41.82075
## 2017.2904 37.58580 33.466810 41.70479 31.286348 43.88525
## 2017.2932 36.56497 32.444664 40.68527 30.263507 42.86643
## 2017.2959 36.52330 32.401685 40.64492 30.219834 42.82677
## 2017.2986 35.89830 31.775374 40.02123 29.592828 42.20377
## 2017.3014 35.96080 31.836562 40.08504 29.653323 42.26828
## 2017.3041 35.89830 31.772752 40.02385 29.588818 42.20778
## 2017.3068 35.14830 31.021441 39.27516 28.836814 41.45979
## 2017.3096 33.81497 29.686798 37.94314 27.501477 40.12846
## 2017.3123 33.21080 29.081322 37.34028 26.895308 39.52629
## 2017.3151 33.64830 29.517513 37.77909 27.330806 39.965804.2.4 Check accuracy
accuracy(climate_auto_f, ts_test)## ME RMSE MAE MPE MAPE MASE
## Training set 0.01624947 1.851854 1.212622 -0.2772843 5.181115 0.474274
## Test set -2.62195810 4.205774 3.563342 -13.6703883 18.427293 1.393674
## ACF1 Theil's U
## Training set 0.002660007 NA
## Test set 0.750725339 2.6592784.3 STLM Model
4.3.1 Create STLM Model
climate_stlm <- stlm(y= ts_train,
s.window = 356,
method = "arima")
summary(climate_stlm$model)## Series: x
## ARIMA(1,1,1)
##
## Coefficients:
## ar1 ma1
## 0.6827 -0.9818
## s.e. 0.0222 0.0070
##
## sigma^2 estimated as 1.776: log likelihood=-2492.66
## AIC=4991.32 AICc=4991.34 BIC=5007.18
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE
## Training set 0.04844167 1.331441 1.013621 -0.07929947 4.019139 0.3964418
## ACF1
## Training set -0.0020636784.3.2 Forecast
climate_stlm_forecast <- forecast(climate_stlm, h = 114)4.3.3 Check Accuracy
accuracy(climate_stlm_forecast, ts_test)## ME RMSE MAE MPE MAPE MASE
## Training set 0.04844167 1.331441 1.013621 -0.1071771 4.393256 0.3964417
## Test set -0.72793616 2.806880 2.294755 -5.1266987 12.153969 0.8975117
## ACF1 Theil's U
## Training set -0.002063678 NA
## Test set 0.723578346 1.7797554.3.4 Visualization
ts_train %>%
autoplot(series = "Actual") +
autolayer(climate_stlm_forecast$fitted, series = "Train") +
autolayer(climate_stlm_forecast$mean, series = "Test")
From the analysis above, we can conclude that we have sucsesfully forecast mean temperature and found STLM as the best model with the lowest error (MAPE ~12.15).
5 Assumption
5.1 No auto-correlation residual
forecast::Acf(climate_stlm$residuals)
Based on acf above we can see there are some autocorellation. We have to check more detail our autocorelaltion is significant or not because our mind can trick us. We do Ljung-box test to make sure.
Box.test(climate_stlm$residuals, type = "Ljung-Box")##
## Box-Ljung test
##
## data: climate_stlm$residuals
## X-squared = 0.0062391, df = 1, p-value = 0.937p-value >0.05 that means there is no autocorrelation.
5.2 Normality residual
hist(climate_stlm$residuals, breaks = 20)
shapiro.test(climate_stlm$residuals)##
## Shapiro-Wilk normality test
##
## data: climate_stlm$residuals
## W = 0.98986, p-value = 0.00000001546p-value < 0.05, our forecast residuals are not distributed normally.
Based on the assumption check, there is no autocorrelation on our forecast residuals (p-value > 0.05), but our forecast’s residuals are not distributed normally, therefore it’s residuals may not be appeared around its mean as seen in the histogram. But, if we inspect the distribution of residuals through a line plot, it is actually resembles the error plot from our time series object decomposition.
In a time series, such errors might emerge from various unpredictable events and is actually quite unavoidable. One strategy to overcome it is to analyze what kinds of unpredictable events that might occur and occurs frequently.