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# Untitled

a guest Feb 20th, 2019 69 Never
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1. #Creating the time series and forecasting
2. batc_haug_ts <- ts(batc_haug.mx)
3. plot.ts(batc_haug_ts, ylab="Log (nr.rec)")
4. batc_haug_ts_forecast_HW <- HoltWinters(batc_haug_ts, gamma=FALSE)
5.
6. batc_haug_ts_forecast_HW #alpha=0.81 and beta=0.10
7. plot(batc_haug_ts_forecast_HW) #the forecast line (red) fits good with the data, however it is lagging some (a bit behind the original data)
8.
9. batc_haug_ts_forecast_HW\$fitted #Level = 4.56, Trend = 0.78
10. HoltWinters(batc_haug_ts, gamma=FALSE, l.start=4.56, b.start=0.78 )
11. batc_haug_ts_forecast2 <- forecast(batc_haug_ts_forecast_HW
12. plot(batc_haug_ts_forecast2, xlab="time", ylab="Log (nr.rec)")
13.
14.
15. batc_haug_ts_forecast2\$residuals <- na.omit(batc_haug_ts_forecast2\$residuals)
16.
17. acf(batc_haug_ts_forecast2\$residuals, lag.max=20)
18. Box.test(batc_haug_ts_forecast2\$residuals, lag=20, type="Ljung-Box")  #p-value=0.1695, thus little evidence of non-zero auto correlation
19.
20. #ARIMA-model by using auto.arima
21. auto.arima(batc_haug_ts) # (1,0,0) 1 paramteres
22. batc_haug_ts_arima <- arima(batc_haug_ts, order = c(1, 0, 0))
23. batc_haug_ts_arima   #AIC=202,15
24. batc_haug_ts_arima_forecast <- forecast(batc_haug_ts_arima)
25. batc_haug_ts_arima_forecast
26. plot(batc_haug_ts_arima_forecast)
27. acf(batc_haug_ts_arima_forecast\$residuals)
28. pacf(batc_haug_ts_arima_forecast\$residuals)
29. Box.test(batc_haug_ts_arima_forecast\$residuals, lag=20, type="Ljung-Box")      #p-vaule=0.3001 --> little evidence of non-zero autocorrelation --> ARIMA (1,0,0) seems to be a good model
30.
31. summary(batc_haug_ts_arima_forecast) #AIC=202,15
32.
33. #By the ACF and PACF there seems to be something happening at lag 7, thus testing again with p or q =7
34.
35. batc_haug_ts_arima2 <- arima(batc_haug_ts, order = c(1, 0, 7))
36. batc_haug_ts_arima2
37. batc_haug_ts_arima2_forecast <- forecast(batc_haug_ts_arima2)
38. batc_haug_ts_arima2_forecast
39. plot(batc_haug_ts_arima2_forecast)
40. acf(batc_haug_ts_arima2_forecast\$residuals)
41. pacf(batc_haug_ts_arima2_forecast\$residuals)
42. Box.test(batc_haug_ts_arima2_forecast\$residuals, lag=20, type="Ljung-Box")    #p-vaule=0.9835 --> little evidence of non-zero autocorrelation --> ARIMA (1,0,7) seems to be a good model
43.
44. summary(batc_haug_ts_arima2_forecast) #AIC = 204,37 thus higher than arima (1,0,0). thus the original autoarima is the best.
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