Sarima.docx

p-value smaller than printed p-value Augmented Dickey-Fuller Test data: d.data Dickey-Fuller = -5.0235, Lag order = 4, p-value = 0.01 alternative hypothesis: stationary

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ARIMA(2,0,2)(1,0,1)[12] with non-zero mean : 64.6204 ARIMA(0,0,0) with non-zero mean : 65.06637

ARIMA(1,0,0)(1,0,0)[12] ARIMA(0,0,1)(0,0,1)[12] ARIMA(0,0,0) ARIMA(1,0,0) ARIMA(1,0,0)(1,0,1)[12] ARIMA(0,0,0)(1,0,0)[12] ARIMA(0,0,1)(1,0,0)[12] ARIMA(1,0,1)(1,0,0)[12] ARIMA(0,0,0)(1,0,0)[12] ARIMA(0,0,0)(1,0,1)[12]

with with with with with with with with with with

non-zero mean non-zero mean zero mean non-zero mean non-zero mean non-zero mean non-zero mean non-zero mean zero mean non-zero mean

: : : : : : : : : :

48.38832 52.24332 446.2903 64.8284 52.43144 44.47428 48.37377 Inf Inf 48.5121

Best model: ARIMA(0,0,0)(1,0,0)[12] with non-zero mean

Series: data.train ARIMA(0,0,0)(1,0,0)[12] with non-zero mean Coefficients: sar1 mean 0.6534 9.6366 s.e. 0.0997 0.0842 sigma^2 estimated as 0.09266: log likelihood=-16.1 AIC=38.19 AICc=38.62 BIC=44.47 Training set error measures: ME RMSE MAE MPE MAPE MASE Training set -0.02052579 0.2992888 0.227509 -0.3119626 2.346429 0.887546 ACF1 Training set 0.05042917

2.5 % 97.5 % sar1 0.4580273 0.8487124 intercept 9.4716271 9.8015703

Box-Ljung test data: arima1$residuals X-squared = 13.846, df = 20, p-value = 0.8382

Box-Ljung test data: arima1$residuals^2 X-squared = 6.1047, df = 20, p-value = 0.9987

Jarque Bera Test data: arima1$residuals X-squared = 9.664, df = 2, p-value = 0.007971

Point Forecast Lo 80 Hi Jan 2017 9.676315 9.286204 Feb 2017 9.686749 9.296638 Mar 2017 9.156576 8.766465 Apr 2017 9.340614 8.950503 May 2017 10.132200 9.742089 Jun 2017 9.561010 9.170899 Jul 2017 9.940042 9.549931 Aug 2017 9.320164 8.930053 Sep 2017 9.545747 9.155636 Oct 2017 9.644985 9.254874 Nov 2017 9.320510 8.930399 Dec 2017 9.487160 9.097049 Jan 2018 9.662548 9.196550 Feb 2018 9.669366 9.203368 Mar 2018 9.322966 8.856969 Apr 2018 9.443211 8.977213 May 2018 9.960410 9.494412 Jun 2018 9.587211 9.121214 Jul 2018 9.834859 9.368861 Aug 2018 9.429850 8.963852 Sep 2018 9.577239 9.111241 Oct 2018 9.642078 9.176080 Nov 2018 9.430076 8.964078 Dec 2018 9.538960 9.072962

80 Lo 95 Hi 10.066426 9.079692 10.076860 9.090126 9.546687 8.559953 9.730725 8.743990 10.522311 9.535577 9.951121 8.964387 10.330153 9.343418 9.710275 8.723541 9.935858 8.949123 10.035096 9.048361 9.710621 8.723887 9.877271 8.890537 10.128546 8.949866 10.135363 8.956684 9.788964 8.610284 9.909209 8.730529 10.426408 9.247728 10.053209 8.874530 10.300857 9.122177 9.895848 8.717168 10.043236 8.864557 10.108076 8.929396 9.896074 8.717394 10.004958 8.826278

95 10.272938 10.283373 9.753199 9.937237 10.728824 10.157633 10.536665 9.916788 10.142370 10.241608 9.917134 10.083783 10.375230 10.382048 10.035648 10.155893 10.673092 10.299893 10.547541 10.142532 10.289921 10.354760 10.142758 10.251642

ME RMSE MAE MPE MAPE MASE Training set -0.02052579 0.2992888 0.2275090 -0.3119626 2.346429 0.887546 Test set -0.31721041 0.4492273 0.3652627 -3.4935098 3.993083 1.424943 ACF1 Theil's U Training set 0.05042917 NA Test set 0.20317884 1.43697