Desertification
Luigi Caputi, 02/02/2023
| Statistics on Desertification and Other climatic Variables |
Basic Statistics The supplied dataset (“Desertification”) consists of 1,1600 observations from 29 localities. Data are organized by monthly values of Wind, Temperature, Rainfall and Destert Storms occorrences per year (from 2003 to 2012). Herein, I will first reorder the data in to have them more handable, and then make four different dataframes, one for each of the four variables.
For each of the variable (Wind, Sandstorms, Rainfall and temperature) a barplot (with stabdard deviations) and a boxplot are produced. Moreover, by stations trends are visualized.
WIND
SANDSTORMS
TEMPERATURE
RAINFALL
Forecasting future Sand Storms.
a Modelling future sand storms using a generalized mixed model
## # A tibble: 29 × 9
## station Meansandstorms sd.x MeanWind sd.y Meantemperature sd.x.x
## <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 Abha 0.0818 0.335 6.27 1.22 28.3 3.76
## 2 Al-Ahsa 1.65 2.84 6.31 1.70 39.9 7.69
## 3 Al-Baha 0.118 0.631 6.19 1.66 32.9 6.45
## 4 Al-Jouf 0.7 1.40 7.55 1.24 34.6 7.99
## 5 Arar 0.327 0.743 8.05 1.41 35.4 8.87
## 6 Bisha 0.264 0.725 4.3 0.934 37.1 4.38
## 7 Dhahran 0.218 0.612 8.15 1.25 38.6 7.91
## 8 Dmmam 0.636 1.22 8.48 1.29 38.6 7.87
## 9 Guriat 0.373 0.876 8.43 2.20 33.6 8.08
## 10 Hafr Elbatten 1.06 1.88 7.67 1.61 37.5 8.25
## # ℹ 19 more rows
## # ℹ 2 more variables: Meanrainfall <dbl>, sd.y.y <dbl>##
## Call:
## glm(formula = Meansandstorms ~ Meantemperature * MeanWind * Meanrainfall,
## family = "gaussian", data = Means)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.47431 -0.21351 -0.05519 0.16530 1.00386
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.568908 21.191347 0.121 0.905
## Meantemperature -0.117260 0.595896 -0.197 0.846
## MeanWind -0.299684 3.257930 -0.092 0.928
## Meanrainfall -0.130819 5.606664 -0.023 0.982
## Meantemperature:MeanWind 0.016331 0.091236 0.179 0.860
## Meantemperature:Meanrainfall 0.016538 0.158125 0.105 0.918
## MeanWind:Meanrainfall -0.058714 0.876495 -0.067 0.947
## Meantemperature:MeanWind:Meanrainfall -0.000132 0.024553 -0.005 0.996
##
## (Dispersion parameter for gaussian family taken to be 0.1336996)
##
## Null deviance: 3.8667 on 27 degrees of freedom
## Residual deviance: 2.6740 on 20 degrees of freedom
## (1 osservazione eliminata a causa di un valore mancante)
## AIC: 31.699
##
## Number of Fisher Scoring iterations: 2## Estimate Std. Error t value
## (Intercept) 2.5689083211 21.19134694 0.121224400
## Meantemperature -0.1172598642 0.59589608 -0.196779049
## MeanWind -0.2996839947 3.25792957 -0.091986026
## Meanrainfall -0.1308188829 5.60666447 -0.023332747
## Meantemperature:MeanWind 0.0163304816 0.09123567 0.178992297
## Meantemperature:Meanrainfall 0.0165381941 0.15812519 0.104589245
## MeanWind:Meanrainfall -0.0587135660 0.87649477 -0.066986784
## Meantemperature:MeanWind:Meanrainfall -0.0001320486 0.02455292 -0.005378125
## Pr(>|t|)
## (Intercept) 0.9047230
## Meantemperature 0.8459863
## MeanWind 0.9276243
## Meanrainfall 0.9816161
## Meantemperature:MeanWind 0.8597446
## Meantemperature:Meanrainfall 0.9177435
## MeanWind:Meanrainfall 0.9472574
## Meantemperature:MeanWind:Meanrainfall 0.9957622## 1 2 3 4 5 6
## -0.14106166 0.64158981 0.30035630 0.43129886 0.55104505 0.16143945
## 7 8 9 10 11 12
## 0.69249316 0.69024334 0.42922862 0.57517857 0.38679940 0.50906440
## 13 14 15 16 17 18
## 0.53594545 0.14343612 0.31765696 0.06662691 0.37518301 0.55625923
## 19 20 21 23 24 25
## 0.63722383 0.48074321 0.53669707 0.42826606 0.53125988 0.11946379
## 26 27 28 29
## 0.18536134 0.14480716 0.35037289 0.53574906b Using the Autoregressive integrated moving average (ARIMA) models predict future values based on past values
Al-Ahsa
##
## #######################
## # KPSS Unit Root Test #
## #######################
##
## Test is of type: mu with 6 lags.
##
## Value of test-statistic is: 1.8605
##
## Critical value for a significance level of:
## 10pct 5pct 2.5pct 1pct
## critical values 0.347 0.463 0.574 0.739##
## ###############################################
## # Augmented Dickey-Fuller Test Unit Root Test #
## ###############################################
##
## Test regression none
##
##
## Call:
## lm(formula = z.diff ~ z.lag.1 - 1 + z.diff.lag)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5.8656 -0.0533 0.0000 1.4332 13.3945
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## z.lag.1 -0.464824 0.094194 -4.935 3.03e-06 ***
## z.diff.lag -0.007108 0.097479 -0.073 0.942
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.83 on 105 degrees of freedom
## Multiple R-squared: 0.2347, Adjusted R-squared: 0.2202
## F-statistic: 16.1 on 2 and 105 DF, p-value: 7.939e-07
##
##
## Value of test-statistic is: -4.9348
##
## Critical values for test statistics:
## 1pct 5pct 10pct
## tau1 -2.58 -1.95 -1.62##
## ARIMA(2,1,2)(1,0,1)[12] with drift : Inf
## ARIMA(0,1,0) with drift : 561.1516
## ARIMA(1,1,0)(1,0,0)[12] with drift : 554.0325
## ARIMA(0,1,1)(0,0,1)[12] with drift : 534.7235
## ARIMA(0,1,0) : 559.1516
## ARIMA(0,1,1) with drift : 535.7758
## ARIMA(0,1,1)(1,0,1)[12] with drift : 536.7672
## ARIMA(0,1,1)(0,0,2)[12] with drift : 536.7203
## ARIMA(0,1,1)(1,0,0)[12] with drift : 534.7544
## ARIMA(0,1,1)(1,0,2)[12] with drift : Inf
## ARIMA(0,1,0)(0,0,1)[12] with drift : 562.533
## ARIMA(1,1,1)(0,0,1)[12] with drift : Inf
## ARIMA(0,1,2)(0,0,1)[12] with drift : Inf
## ARIMA(1,1,0)(0,0,1)[12] with drift : 555.0102
## ARIMA(1,1,2)(0,0,1)[12] with drift : Inf
## ARIMA(0,1,1)(0,0,1)[12] : 532.9767
## ARIMA(0,1,1) : 533.9156
## ARIMA(0,1,1)(1,0,1)[12] : 534.8942
## ARIMA(0,1,1)(0,0,2)[12] : 534.9761
## ARIMA(0,1,1)(1,0,0)[12] : 532.9619
## ARIMA(0,1,1)(2,0,0)[12] : 534.9602
## ARIMA(0,1,1)(2,0,1)[12] : Inf
## ARIMA(0,1,0)(1,0,0)[12] : 560.2934
## ARIMA(1,1,1)(1,0,0)[12] : 525.8295
## ARIMA(1,1,1) : 525.1277
## ARIMA(1,1,1)(0,0,1)[12] : 526.0592
## ARIMA(1,1,1)(1,0,1)[12] : 526.7145
## ARIMA(1,1,0) : 554.841
## ARIMA(2,1,1) : 524.7834
## ARIMA(2,1,1)(1,0,0)[12] : 526.6345
## ARIMA(2,1,1)(0,0,1)[12] : 526.6719
## ARIMA(2,1,1)(1,0,1)[12] : 527.6806
## ARIMA(2,1,0) : 552.7808
## ARIMA(3,1,1) : 522.1566
## ARIMA(3,1,1)(1,0,0)[12] : 523.6693
## ARIMA(3,1,1)(0,0,1)[12] : 523.7121
## ARIMA(3,1,1)(1,0,1)[12] : 525.4025
## ARIMA(3,1,0) : 530.9177
## ARIMA(4,1,1) : 520.9456
## ARIMA(4,1,1)(1,0,0)[12] : 522.7825
## ARIMA(4,1,1)(0,0,1)[12] : 522.788
## ARIMA(4,1,1)(1,0,1)[12] : 524.7285
## ARIMA(4,1,0) : 532.3472
## ARIMA(5,1,1) : 520.9891
## ARIMA(4,1,2) : Inf
## ARIMA(3,1,2) : Inf
## ARIMA(5,1,0) : 531.8403
## ARIMA(5,1,2) : Inf
## ARIMA(4,1,1) with drift : Inf
##
## Best model: ARIMA(4,1,1)## Series: AA_train[, 5]
## ARIMA(4,1,1)
##
## Coefficients:
## ar1 ar2 ar3 ar4 ma1
## 0.3667 -0.0702 -0.2438 0.1908 -0.9362
## s.e. 0.1109 0.1000 0.0996 0.1051 0.0556
##
## sigma^2 = 6.711: log likelihood = -254.47
## AIC=520.95 AICc=521.78 BIC=537.04## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## Feb 2012 0.8582904 -2.461645 4.178226 -4.219112 5.935693
## Mar 2012 0.7360849 -2.878429 4.350599 -4.791837 6.264007
## Apr 2012 0.4574103 -3.191901 4.106722 -5.123730 6.038550
## May 2012 0.5891722 -3.096108 4.274452 -5.046978 6.225322
## Jun 2012 0.6598181 -3.035576 4.355213 -4.991800 6.311436
## Jul 2012 0.7210951 -3.007740 4.449931 -4.981667 6.423857
## Aug 2012 0.6533017 -3.122951 4.429555 -5.121979 6.428582
## Sep 2012 0.6320557 -3.151255 4.415367 -5.154019 6.418131
## Oct 2012 0.6275668 -3.160280 4.415413 -5.165445 6.420578
## Nov 2012 0.6556348 -3.138208 4.449478 -5.146548 6.457817
## Dec 2012 0.6584866 -3.150078 4.467051 -5.166211 6.483184
## Jan 2013 0.6546012 -3.167255 4.476457 -5.190423 6.499625
## Feb 2013 0.6452761 -3.187454 4.478006 -5.216379 6.506931
## Mar 2013 0.6467901 -3.194375 4.487955 -5.227764 6.521344
## Apr 2013 0.6494917 -3.201226 4.500210 -5.239673 6.538657
## May 2013 0.6519083 -3.209255 4.513072 -5.253232 6.557048
## Jun 2013 0.6504561 -3.221577 4.522489 -5.271307 6.572219
## Jul 2013 0.6493841 -3.232809 4.531577 -5.287918 6.586686
## Aug 2013 0.6490193 -3.243040 4.541079 -5.303372 6.601411
## Sep 2013 0.6497760 -3.252141 4.551693 -5.317691 6.617243
## Oct 2013 0.6500634 -3.261954 4.562080 -5.332850 6.632977
## Nov 2013 0.6500000 -3.272128 4.572128 -5.348377 6.648377
## Dec 2013 0.6497025 -3.282450 4.581855 -5.364006 6.663411
## Jan 2014 0.6496721 -3.292393 4.591738 -5.379197 6.678541
Hafr Elbatten
##
## #######################
## # KPSS Unit Root Test #
## #######################
##
## Test is of type: mu with 6 lags.
##
## Value of test-statistic is: 1.8605
##
## Critical value for a significance level of:
## 10pct 5pct 2.5pct 1pct
## critical values 0.347 0.463 0.574 0.739##
## ###############################################
## # Augmented Dickey-Fuller Test Unit Root Test #
## ###############################################
##
## Test regression none
##
##
## Call:
## lm(formula = z.diff ~ z.lag.1 - 1 + z.diff.lag)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5.8656 -0.0533 0.0000 1.4332 13.3945
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## z.lag.1 -0.464824 0.094194 -4.935 3.03e-06 ***
## z.diff.lag -0.007108 0.097479 -0.073 0.942
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.83 on 105 degrees of freedom
## Multiple R-squared: 0.2347, Adjusted R-squared: 0.2202
## F-statistic: 16.1 on 2 and 105 DF, p-value: 7.939e-07
##
##
## Value of test-statistic is: -4.9348
##
## Critical values for test statistics:
## 1pct 5pct 10pct
## tau1 -2.58 -1.95 -1.62##
## ARIMA(2,1,2)(1,0,1)[12] with drift : Inf
## ARIMA(0,1,0) with drift : 561.1516
## ARIMA(1,1,0)(1,0,0)[12] with drift : 554.0325
## ARIMA(0,1,1)(0,0,1)[12] with drift : 534.7235
## ARIMA(0,1,0) : 559.1516
## ARIMA(0,1,1) with drift : 535.7758
## ARIMA(0,1,1)(1,0,1)[12] with drift : 536.7672
## ARIMA(0,1,1)(0,0,2)[12] with drift : 536.7203
## ARIMA(0,1,1)(1,0,0)[12] with drift : 534.7544
## ARIMA(0,1,1)(1,0,2)[12] with drift : Inf
## ARIMA(0,1,0)(0,0,1)[12] with drift : 562.533
## ARIMA(1,1,1)(0,0,1)[12] with drift : Inf
## ARIMA(0,1,2)(0,0,1)[12] with drift : Inf
## ARIMA(1,1,0)(0,0,1)[12] with drift : 555.0102
## ARIMA(1,1,2)(0,0,1)[12] with drift : Inf
## ARIMA(0,1,1)(0,0,1)[12] : 532.9767
## ARIMA(0,1,1) : 533.9156
## ARIMA(0,1,1)(1,0,1)[12] : 534.8942
## ARIMA(0,1,1)(0,0,2)[12] : 534.9761
## ARIMA(0,1,1)(1,0,0)[12] : 532.9619
## ARIMA(0,1,1)(2,0,0)[12] : 534.9602
## ARIMA(0,1,1)(2,0,1)[12] : Inf
## ARIMA(0,1,0)(1,0,0)[12] : 560.2934
## ARIMA(1,1,1)(1,0,0)[12] : 525.8295
## ARIMA(1,1,1) : 525.1277
## ARIMA(1,1,1)(0,0,1)[12] : 526.0592
## ARIMA(1,1,1)(1,0,1)[12] : 526.7145
## ARIMA(1,1,0) : 554.841
## ARIMA(2,1,1) : 524.7834
## ARIMA(2,1,1)(1,0,0)[12] : 526.6345
## ARIMA(2,1,1)(0,0,1)[12] : 526.6719
## ARIMA(2,1,1)(1,0,1)[12] : 527.6806
## ARIMA(2,1,0) : 552.7808
## ARIMA(3,1,1) : 522.1566
## ARIMA(3,1,1)(1,0,0)[12] : 523.6693
## ARIMA(3,1,1)(0,0,1)[12] : 523.7121
## ARIMA(3,1,1)(1,0,1)[12] : 525.4025
## ARIMA(3,1,0) : 530.9177
## ARIMA(4,1,1) : 520.9456
## ARIMA(4,1,1)(1,0,0)[12] : 522.7825
## ARIMA(4,1,1)(0,0,1)[12] : 522.788
## ARIMA(4,1,1)(1,0,1)[12] : 524.7285
## ARIMA(4,1,0) : 532.3472
## ARIMA(5,1,1) : 520.9891
## ARIMA(4,1,2) : Inf
## ARIMA(3,1,2) : Inf
## ARIMA(5,1,0) : 531.8403
## ARIMA(5,1,2) : Inf
## ARIMA(4,1,1) with drift : Inf
##
## Best model: ARIMA(4,1,1)## Series: AA_train[, 5]
## ARIMA(4,1,1)
##
## Coefficients:
## ar1 ar2 ar3 ar4 ma1
## 0.3667 -0.0702 -0.2438 0.1908 -0.9362
## s.e. 0.1109 0.1000 0.0996 0.1051 0.0556
##
## sigma^2 = 6.711: log likelihood = -254.47
## AIC=520.95 AICc=521.78 BIC=537.04## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## Feb 2012 0.8582904 -2.461645 4.178226 -4.219112 5.935693
## Mar 2012 0.7360849 -2.878429 4.350599 -4.791837 6.264007
## Apr 2012 0.4574103 -3.191901 4.106722 -5.123730 6.038550
## May 2012 0.5891722 -3.096108 4.274452 -5.046978 6.225322
## Jun 2012 0.6598181 -3.035576 4.355213 -4.991800 6.311436
## Jul 2012 0.7210951 -3.007740 4.449931 -4.981667 6.423857
## Aug 2012 0.6533017 -3.122951 4.429555 -5.121979 6.428582
## Sep 2012 0.6320557 -3.151255 4.415367 -5.154019 6.418131
## Oct 2012 0.6275668 -3.160280 4.415413 -5.165445 6.420578
## Nov 2012 0.6556348 -3.138208 4.449478 -5.146548 6.457817
## Dec 2012 0.6584866 -3.150078 4.467051 -5.166211 6.483184
## Jan 2013 0.6546012 -3.167255 4.476457 -5.190423 6.499625
## Feb 2013 0.6452761 -3.187454 4.478006 -5.216379 6.506931
## Mar 2013 0.6467901 -3.194375 4.487955 -5.227764 6.521344
## Apr 2013 0.6494917 -3.201226 4.500210 -5.239673 6.538657
## May 2013 0.6519083 -3.209255 4.513072 -5.253232 6.557048
## Jun 2013 0.6504561 -3.221577 4.522489 -5.271307 6.572219
## Jul 2013 0.6493841 -3.232809 4.531577 -5.287918 6.586686
## Aug 2013 0.6490193 -3.243040 4.541079 -5.303372 6.601411
## Sep 2013 0.6497760 -3.252141 4.551693 -5.317691 6.617243
## Oct 2013 0.6500634 -3.261954 4.562080 -5.332850 6.632977
## Nov 2013 0.6500000 -3.272128 4.572128 -5.348377 6.648377
## Dec 2013 0.6497025 -3.282450 4.581855 -5.364006 6.663411
## Jan 2014 0.6496721 -3.292393 4.591738 -5.379197 6.678541
Qaisumah
##
## #######################
## # KPSS Unit Root Test #
## #######################
##
## Test is of type: mu with 6 lags.
##
## Value of test-statistic is: 1.8618
##
## Critical value for a significance level of:
## 10pct 5pct 2.5pct 1pct
## critical values 0.347 0.463 0.574 0.739##
## ###############################################
## # Augmented Dickey-Fuller Test Unit Root Test #
## ###############################################
##
## Test regression none
##
##
## Call:
## lm(formula = z.diff ~ z.lag.1 - 1 + z.diff.lag)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.7051 -0.2061 0.0000 0.8109 12.4934
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## z.lag.1 -0.54058 0.11144 -4.851 4.29e-06 ***
## z.diff.lag -0.20612 0.09549 -2.158 0.0332 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.956 on 105 degrees of freedom
## Multiple R-squared: 0.3685, Adjusted R-squared: 0.3565
## F-statistic: 30.63 on 2 and 105 DF, p-value: 3.31e-11
##
##
## Value of test-statistic is: -4.8508
##
## Critical values for test statistics:
## 1pct 5pct 10pct
## tau1 -2.58 -1.95 -1.62##
## ARIMA(2,1,2)(1,0,1)[12] with drift : Inf
## ARIMA(0,1,0) with drift : 501.982
## ARIMA(1,1,0)(1,0,0)[12] with drift : 476.4037
## ARIMA(0,1,1)(0,0,1)[12] with drift : 439.867
## ARIMA(0,1,0) : 499.982
## ARIMA(0,1,1) with drift : 437.888
## ARIMA(0,1,1)(1,0,0)[12] with drift : 439.8678
## ARIMA(0,1,1)(1,0,1)[12] with drift : 441.6647
## ARIMA(1,1,1) with drift : 439.5038
## ARIMA(0,1,2) with drift : 439.3593
## ARIMA(1,1,0) with drift : 476.4333
## ARIMA(1,1,2) with drift : 438.2166
## ARIMA(0,1,1) : 435.8901
## ARIMA(0,1,1)(1,0,0)[12] : 437.8704
## ARIMA(0,1,1)(0,0,1)[12] : 437.8696
## ARIMA(0,1,1)(1,0,1)[12] : 439.6726
## ARIMA(1,1,1) : 437.504
## ARIMA(0,1,2) : 437.3593
## ARIMA(1,1,0) : 474.4333
## ARIMA(1,1,2) : 436.2948
##
## Best model: ARIMA(0,1,1)## Series: AA_train[, 5]
## ARIMA(0,1,1)
##
## Coefficients:
## ma1
## -0.8727
## s.e. 0.0429
##
## sigma^2 = 3.181: log likelihood = -215.95
## AIC=435.89 AICc=436 BIC=441.25## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## Feb 2012 0.310662 -1.974959 2.596283 -3.184894 3.806218
## Mar 2012 0.310662 -1.993411 2.614735 -3.213114 3.834438
## Apr 2012 0.310662 -2.011716 2.633040 -3.241109 3.862433
## May 2012 0.310662 -2.029878 2.651202 -3.268885 3.890209
## Jun 2012 0.310662 -2.047900 2.669224 -3.296447 3.917771
## Jul 2012 0.310662 -2.065785 2.687109 -3.323800 3.945124
## Aug 2012 0.310662 -2.083537 2.704861 -3.350949 3.972273
## Sep 2012 0.310662 -2.101158 2.722482 -3.377898 3.999222
## Oct 2012 0.310662 -2.118651 2.739975 -3.404652 4.025976
## Nov 2012 0.310662 -2.136019 2.757343 -3.431214 4.052538
## Dec 2012 0.310662 -2.153265 2.774589 -3.457589 4.078913
## Jan 2013 0.310662 -2.170391 2.791715 -3.483781 4.105105
## Feb 2013 0.310662 -2.187399 2.808723 -3.509793 4.131117
## Mar 2013 0.310662 -2.204293 2.825617 -3.535629 4.156953
## Apr 2013 0.310662 -2.221073 2.842397 -3.561293 4.182617
## May 2013 0.310662 -2.237744 2.859068 -3.586788 4.208112
## Jun 2013 0.310662 -2.254305 2.875629 -3.612117 4.233441
## Jul 2013 0.310662 -2.270761 2.892085 -3.637284 4.258608
## Aug 2013 0.310662 -2.287112 2.908436 -3.662291 4.283615
## Sep 2013 0.310662 -2.303361 2.924686 -3.687142 4.308466
## Oct 2013 0.310662 -2.319510 2.940834 -3.711839 4.333163
## Nov 2013 0.310662 -2.335560 2.956884 -3.736386 4.357710
## Dec 2013 0.310662 -2.351514 2.972838 -3.760785 4.382109
## Jan 2014 0.310662 -2.367372 2.988696 -3.785038 4.406362
Rafha
##
## #######################
## # KPSS Unit Root Test #
## #######################
##
## Test is of type: mu with 6 lags.
##
## Value of test-statistic is: 1.8619
##
## Critical value for a significance level of:
## 10pct 5pct 2.5pct 1pct
## critical values 0.347 0.463 0.574 0.739##
## ###############################################
## # Augmented Dickey-Fuller Test Unit Root Test #
## ###############################################
##
## Test regression none
##
##
## Call:
## lm(formula = z.diff ~ z.lag.1 - 1 + z.diff.lag)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.0453 -0.2844 0.0000 1.0000 6.0000
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## z.lag.1 -0.39501 0.09461 -4.175 6.16e-05 ***
## z.diff.lag -0.18959 0.09582 -1.979 0.0505 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.467 on 105 degrees of freedom
## Multiple R-squared: 0.2709, Adjusted R-squared: 0.257
## F-statistic: 19.51 on 2 and 105 DF, p-value: 6.258e-08
##
##
## Value of test-statistic is: -4.1753
##
## Critical values for test statistics:
## 1pct 5pct 10pct
## tau1 -2.58 -1.95 -1.62##
## ARIMA(2,1,2)(1,0,1)[12] with drift : 383.1335
## ARIMA(0,1,0) with drift : 424.3704
## ARIMA(1,1,0)(1,0,0)[12] with drift : 409.9084
## ARIMA(0,1,1)(0,0,1)[12] with drift : 382.6348
## ARIMA(0,1,0) : 422.3704
## ARIMA(0,1,1) with drift : 380.9847
## ARIMA(0,1,1)(1,0,0)[12] with drift : 382.6789
## ARIMA(0,1,1)(1,0,1)[12] with drift : 384.477
## ARIMA(1,1,1) with drift : 381.9588
## ARIMA(0,1,2) with drift : 381.7438
## ARIMA(1,1,0) with drift : 408.9989
## ARIMA(1,1,2) with drift : 383.4506
## ARIMA(0,1,1) : 378.9848
## ARIMA(0,1,1)(1,0,0)[12] : 380.679
## ARIMA(0,1,1)(0,0,1)[12] : 380.6349
## ARIMA(0,1,1)(1,0,1)[12] : 382.4775
## ARIMA(1,1,1) : 379.9591
## ARIMA(0,1,2) : 379.7441
## ARIMA(1,1,0) : 406.9989
## ARIMA(1,1,2) : 381.4507
##
## Best model: ARIMA(0,1,1)## Series: AA_train[, 5]
## ARIMA(0,1,1)
##
## Coefficients:
## ma1
## -0.8154
## s.e. 0.0521
##
## sigma^2 = 1.884: log likelihood = -187.49
## AIC=378.98 AICc=379.1 BIC=384.35## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## Feb 2012 0.2099093 -1.549121 1.968940 -2.480296 2.900114
## Mar 2012 0.2099093 -1.578831 1.998650 -2.525734 2.945552
## Apr 2012 0.2099093 -1.608056 2.027875 -2.570429 2.990247
## May 2012 0.2099093 -1.636818 2.056637 -2.614417 3.034235
## Jun 2012 0.2099093 -1.665139 2.084958 -2.657730 3.077549
## Jul 2012 0.2099093 -1.693039 2.112857 -2.700399 3.120217
## Aug 2012 0.2099093 -1.720535 2.140354 -2.742451 3.162269
## Sep 2012 0.2099093 -1.747646 2.167464 -2.783912 3.203731
## Oct 2012 0.2099093 -1.774385 2.194204 -2.824808 3.244626
## Nov 2012 0.2099093 -1.800770 2.220588 -2.865159 3.284977
## Dec 2012 0.2099093 -1.826812 2.246631 -2.904988 3.324806
## Jan 2013 0.2099093 -1.852526 2.272345 -2.944313 3.364132
## Feb 2013 0.2099093 -1.877923 2.297742 -2.983155 3.402973
## Mar 2013 0.2099093 -1.903015 2.322833 -3.021529 3.441348
## Apr 2013 0.2099093 -1.927812 2.347631 -3.059454 3.479272
## May 2013 0.2099093 -1.952325 2.372144 -3.096943 3.516761
## Jun 2013 0.2099093 -1.976563 2.396382 -3.134012 3.553830
## Jul 2013 0.2099093 -2.000536 2.420354 -3.170674 3.590493
## Aug 2013 0.2099093 -2.024251 2.444069 -3.206944 3.626762
## Sep 2013 0.2099093 -2.047717 2.467535 -3.242832 3.662651
## Oct 2013 0.2099093 -2.070942 2.490760 -3.278351 3.698170
## Nov 2013 0.2099093 -2.093932 2.513751 -3.313512 3.733331
## Dec 2013 0.2099093 -2.116695 2.536514 -3.348326 3.768144
## Jan 2014 0.2099093 -2.139238 2.559057 -3.382802 3.802620
Sulayel
##
## #######################
## # KPSS Unit Root Test #
## #######################
##
## Test is of type: mu with 6 lags.
##
## Value of test-statistic is: 1.862
##
## Critical value for a significance level of:
## 10pct 5pct 2.5pct 1pct
## critical values 0.347 0.463 0.574 0.739##
## ###############################################
## # Augmented Dickey-Fuller Test Unit Root Test #
## ###############################################
##
## Test regression none
##
##
## Call:
## lm(formula = z.diff ~ z.lag.1 - 1 + z.diff.lag)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.8400 -0.3058 0.0000 0.5958 5.3885
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## z.lag.1 -0.29000 0.08493 -3.415 0.000909 ***
## z.diff.lag -0.30576 0.09292 -3.291 0.001361 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.343 on 105 degrees of freedom
## Multiple R-squared: 0.2828, Adjusted R-squared: 0.2692
## F-statistic: 20.7 on 2 and 105 DF, p-value: 2.633e-08
##
##
## Value of test-statistic is: -3.4147
##
## Critical values for test statistics:
## 1pct 5pct 10pct
## tau1 -2.58 -1.95 -1.62##
## ARIMA(2,1,2)(1,0,1)[12] with drift : 372.4602
## ARIMA(0,1,0) with drift : 407.0231
## ARIMA(1,1,0)(1,0,0)[12] with drift : 379.3015
## ARIMA(0,1,1)(0,0,1)[12] with drift : 365.6934
## ARIMA(0,1,0) : 405.0231
## ARIMA(0,1,1) with drift : 366.8719
## ARIMA(0,1,1)(1,0,1)[12] with drift : 367.5868
## ARIMA(0,1,1)(0,0,2)[12] with drift : 367.5732
## ARIMA(0,1,1)(1,0,0)[12] with drift : 365.986
## ARIMA(0,1,1)(1,0,2)[12] with drift : 369.5694
## ARIMA(0,1,0)(0,0,1)[12] with drift : 406.3063
## ARIMA(1,1,1)(0,0,1)[12] with drift : 367.4671
## ARIMA(0,1,2)(0,0,1)[12] with drift : 367.51
## ARIMA(1,1,0)(0,0,1)[12] with drift : 379.2245
## ARIMA(1,1,2)(0,0,1)[12] with drift : 369.3311
## ARIMA(0,1,1)(0,0,1)[12] : 363.6935
## ARIMA(0,1,1) : 364.8729
## ARIMA(0,1,1)(1,0,1)[12] : 365.5875
## ARIMA(0,1,1)(0,0,2)[12] : 365.5739
## ARIMA(0,1,1)(1,0,0)[12] : 363.9861
## ARIMA(0,1,1)(1,0,2)[12] : 367.57
## ARIMA(0,1,0)(0,0,1)[12] : 404.3064
## ARIMA(1,1,1)(0,0,1)[12] : 365.4672
## ARIMA(0,1,2)(0,0,1)[12] : 365.5101
## ARIMA(1,1,0)(0,0,1)[12] : 377.2252
## ARIMA(1,1,2)(0,0,1)[12] : 367.3314
##
## Best model: ARIMA(0,1,1)(0,0,1)[12]## Series: AA_train[, 5]
## ARIMA(0,1,1)(0,0,1)[12]
##
## Coefficients:
## ma1 sma1
## -0.7316 -0.1725
## s.e. 0.0690 0.0947
##
## sigma^2 = 1.62: log likelihood = -178.85
## AIC=363.69 AICc=363.92 BIC=371.74## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## Feb 2012 0.10372101 -1.527297 1.734739 -2.390705 2.598147
## Mar 2012 0.13450157 -1.554244 1.823247 -2.448212 2.717215
## Apr 2012 0.13522903 -1.609335 1.879793 -2.532851 2.803310
## May 2012 -0.03202172 -1.830673 1.766630 -2.782821 2.718778
## Jun 2012 0.14044984 -1.710709 1.991609 -2.690653 2.971553
## Jul 2012 0.11067597 -1.791542 2.012893 -2.798515 3.019867
## Aug 2012 0.13961916 -1.812322 2.091560 -2.845617 3.124855
## Sep 2012 0.14048293 -1.859946 2.140912 -2.918909 3.199875
## Oct 2012 -0.03228364 -2.080053 2.015486 -3.164076 3.099509
## Nov 2012 0.14052435 -1.953515 2.234564 -3.062033 3.343081
## Dec 2012 0.13954608 -1.999763 2.278855 -3.132245 3.411337
## Jan 2013 0.14044154 -2.043199 2.324082 -3.199149 3.480032
## Feb 2013 0.11630173 -2.072933 2.305537 -3.231844 3.464448
## Mar 2013 0.11630173 -2.102702 2.335305 -3.277371 3.509975
## Apr 2013 0.11630173 -2.132076 2.364679 -3.322295 3.554899
## May 2013 0.11630173 -2.161071 2.393675 -3.366640 3.599243
## Jun 2013 0.11630173 -2.189702 2.422306 -3.410427 3.643031
## Jul 2013 0.11630173 -2.217982 2.450586 -3.453677 3.686281
## Aug 2013 0.11630173 -2.245923 2.478527 -3.496410 3.729013
## Sep 2013 0.11630173 -2.273538 2.506141 -3.538643 3.771246
## Oct 2013 0.11630173 -2.300837 2.533440 -3.580393 3.812996
## Nov 2013 0.11630173 -2.327831 2.560435 -3.621677 3.854281
## Dec 2013 0.11630173 -2.354531 2.587134 -3.662510 3.895114
## Jan 2014 0.11630173 -2.380944 2.613548 -3.702907 3.935510