Tau2 dating

In my previous tutorial Structural Changes in Global Warming I introduced the strucchange package and some basic examples to date structural breaks in time series.

In the present tutorial, I am going to show how dating structural changes (if any) and then Intervention Analysis can help in finding better ARIMA models.

tau2 dating-55

seasonal = TRUE, so that models search is not restricted to non seasonal models ARIMA(0,1,0) : -301.4365 ARIMA(0,1,0) with drift : -299.3722 ARIMA(0,1,1) : -328.9381 ARIMA(0,1,1) with drift : -326.9276 ARIMA(0,1,2) : -329.4061 ARIMA(0,1,2) with drift : Inf ARIMA(0,1,3) : -327.2841 ARIMA(0,1,3) with drift : Inf ARIMA(0,1,4) : -325.7604 ARIMA(0,1,4) with drift : Inf ARIMA(0,1,5) : -323.4805 ARIMA(0,1,5) with drift : Inf ARIMA(1,1,0) : -312.8106 ARIMA(1,1,0) with drift : -310.7155 ARIMA(1,1,1) : -329.5727 ARIMA(1,1,1) with drift : Inf ARIMA(1,1,2) : -327.3821 ARIMA(1,1,2) with drift : Inf ARIMA(1,1,3) : -325.1085 ARIMA(1,1,3) with drift : Inf ARIMA(1,1,4) : -323.446 ARIMA(1,1,4) with drift : Inf ARIMA(2,1,0) : -317.1234 ARIMA(2,1,0) with drift : -314.9816 ARIMA(2,1,1) : -327.3795 ARIMA(2,1,1) with drift : Inf ARIMA(2,1,2) : -325.0859 ARIMA(2,1,2) with drift : Inf ARIMA(2,1,3) : -322.9714 ARIMA(2,1,3) with drift : Inf ARIMA(3,1,0) : -315.9114 ARIMA(3,1,0) with drift : -313.7128 ARIMA(3,1,1) : -325.1497 ARIMA(3,1,1) with drift : Inf ARIMA(3,1,2) : -323.1363 ARIMA(3,1,2) with drift : Inf ARIMA(4,1,0) : -315.3018 ARIMA(4,1,0) with drift : -313.0426 ARIMA(4,1,1) : -324.2463 ARIMA(4,1,1) with drift : -322.0252 ARIMA(5,1,0) : -315.1075 ARIMA(5,1,0) with drift : -312.7776 Series: excess_ts ARIMA(1,1,1) Coefficients: ar1 ma1 0.2224 -0.9258 s.e.

That suggests the presence of a seasonal component with period = 10. First let us verify if regression against a constant is significative for our time series.

Optimal (m 1)-segment partition: Call: breakpoints.formula(formula = excess_ts ~ 1) Breakpoints at observation number: m = 1 42 m = 2 20 42 m = 3 20 35 48 m = 4 20 35 50 66 m = 5 17 30 42 56 69 Corresponding to breakdates: m = 1 1670 m = 2 1648 1670 m = 3 1648 1663 1676 m = 4 1648 1663 1678 1694 m = 5 1645 1658 1670 1684 1697 Fit: m 0 1 2 3 4 5 RSS 0.07912 0.06840 0.06210 0.06022 0.05826 0.05894 BIC -327.84807 -330.97945 -330.08081 -323.78985 -317.68933 -307.92410 The BIC minimum value is reached when m = 1, hence just one break point is determined corresponding to year 1670.

Error t value Pr(|t|) 1 -0.01465 0.05027 -0.291 0.771802 lag1 -0.71838 0.13552 -5.301 1.87e-06 *** lag2 -0.66917 0.16431 -4.073 0.000143 *** lag3 -0.58640 0.18567 -3.158 0.002519 ** lag4 -0.56529 0.19688 -2.871 0.005700 ** lag5 -0.58489 0.20248 -2.889 0.005432 ** lag6 -0.60278 0.20075 -3.003 0.003944 ** lag7 -0.43509 0.20012 -2.174 0.033786 * lag8 -0.28608 0.19283 -1.484 0.143335 lag9 -0.14212 0.18150 -0.783 0.436769 lag10 0.13232 0.15903 0.832 0.408801 lag11 -0.07234 0.12774 -0.566 0.573346 --- Signif.

codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 0.03026 on 58 degrees of freedom Multiple R-squared: 0.4638, Adjusted R-squared: 0.3529 F-statistic: 4.181 on 12 and 58 DF, p-value: 0.0001034 Value of test-statistic is: -0.2914 Critical values for test statistics: 1pct 5pct 10pct tau1 -2.6 -1.95 -1.61Title: Augmented Dickey-Fuller Unit Root Test Test Results: Test regression drift Call: lm(formula = ~ 1 1 lag) Residuals: Min 1Q Median 3Q Max -0.051868 -0.018870 -0.005227 0.019503 0.067936 Coefficients: Estimate Std.

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