Time series and forecasting in R - maths …

1 Time series and forecasting in R 1 Time series and forecasting in R 2. Outline Time series and forecasting 1 Time series objects in R 2 Basic time series functionality 3 The forecast package Rob J hyndman 4 Exponential smoothing 29 June 2008. 5 ARIMA modelling 6 More from the forecast package 7 Time series packages on CRAN. Time series and forecasting in R Time series objects 4 Time series and forecasting in R Time series objects 5. Australian GDP Australian GDP. ausgdp <- ts(scan(" "),frequency=4, 7500. start=1971+2/4) > plot(ausgdp). Class: ts 7000. Print and plotting methods available.

2 > ausgdp 6500. Qtr1 Qtr2 Qtr3 Qtr4. ausgdp 6000. 1971 4612 4651. 1972 4645 4615 4645 4722. 5500. 1973 4780 4830 4887 4933. 1974 4921 4875 4867 4905. 5000. 1975 4938 4934 4942 4979. 4500. 1976 5028 5079 5112 5127. 1975 1980 1985 1990 1995. 1977 5130 5101 5072 5069. Time 1978 5100 5166 5244 5312. 1979 5349 5370 5388 5396. 1980 5388 5403 5442 5482. Time series and forecasting in R Time series objects 6 Time series and forecasting in R Time series objects 7. Australian beer production Australian beer production 180. > beer Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec 1991 164 148 152 144 155 125 153 146 138 190 192 192.

3 160. beer 1992 147 133 163 150 129 131 145 137 138 168 176 188. 1993 139 143 150 154 137 129 128 140 143 151 177 184. 1994 151 134 164 126 131 125 127 143 143 160 190 182. 140. 1995 138 136 152 127 151 130 119 153. 120. > plot(beer). 1991 1992 1993 1994 1995. Time Time series and forecasting in R Basic time series functionality 9 Time series and forecasting in R Basic time series functionality 10. Lag plots Lag plots > (beer,lags=12). 100 120 140 160 180 200 100 120 140 160 180 200. 12 47 11. 10 12 47 11 10 1147 10 12. 24 24 24. 180. 48 36 36. 48 48 36. 3523 23 35 35 23.

4 22 22 22. 160. 39 115 39. 15 1 39 15 1. beer beer beer 46 46 46. 5 28 37 28 7 5 5. 515337 34 53 51 3 37 34 328. 3751 16 34. 53 7. (x, lags = 1, layout = NULL, 16 16 27. 1319. 8 227 2 13 8. 27. 13 2 8. 19 19. 140. 33 4 45. 44 26 4 26 44 33 45 26 4 45. 33 44. 32 32 32. 20 25 50. 29 49 21 9 29. 50. 25. 49 20 21 9 49 29 50. 25 20 21 9. 38. 14 38 14 1438. 54 413017 18 41 18 18 41. 3143 52 17 54. 3043. 31 52 40 17 30 31 43. 4240 6 40 52 426 6 42. 120. = 1:lags, main = NULL, 55. lag 1 lag 2 lag 3. 10 12 11 12 11 10 11. 12 10. 47. 24 47 24 24 47. 180. 36. 48 36 48 36 48. 22. 23 35 35 23.)

5 22. 35 23. 22. asp = 1, diag = TRUE, 160. 39 15 1 1 15 39 15 39 1. beer beer beer 46 46 46. 528 283 51 5 5. 51 3 7 7 37 28. 27373416 37 16. 27 34 34. 37 27 16. = "gray", type = "p", 2 13 8 13 8 2 8 19 132. 19 19. 140. 26 45 4 33 44 26 33 4. 45. 44 4426 45 33 4. 25 32 25 32 25 32 20 21. 2129 9 49 20 50 38499 2021 29 49 9 29. 38 50. 14 14 14 38. 50. 18 41 17 18 18. 17 41 30 31 30 43. 31 31 17 30 41. 40 52 42. 43. 6 40 426. 43 40 42 6. 120. 11. 10. 47. 24. 12. lag 4. 47 10 12 11. 24. lag 5. 11. 12 10 47. 24. lag 6. oma = NULL, ask = NULL, 180. 48 36 36 48 36. = (n <= 150), labels = , 3523 35.

6 23 2335. 22 22 22. 160. 1 39 15 1 15 39 39 151. beer beer beer 46 46 46. 28 5 5 28 3 5 28. 347 37 27 16 3 34 37 7. 27 16 34 16. 7 37 27. 3. 132 13 2 13 2..). 19 8 8. 19 8. 4 4419. 140. 33. 45 26 44 4 4433 26. 45 4 33 45 26. 25 2021 32 329 32. 949 29 21 25 2920 2192920 25. 14 38 38 14 14 38. 18 30 41 17 3041 18 41 17 18 30. 31. 43 17 43 31 31. 43. 42 6 40 642 40 40 42 6. 120. lag 7 lag 8 lag 9. 11. 10 12 10 11 12 10 11 12. 24 24 24. 180. 36 36 36. 35. 23 23 35 23 35. 22 22 22. 160. 39. 15 1 39 15 1 39. 115. beer beer beer 46. 5 5 285. 7 28 34 3 37 73 28. 37 7 16 3427. 3. 16 27.

7 2 27 34 216 37. 2 813. 8 19 13 19 8 13 19. 140. 45 33444 26 44 33 26. 45 4 26 33 444. 32 25 32 25 32. 21. 20 9 29 20 921. 29 29 92021 25. 38 14 38. 14 38 14. 30 31 18. 41 4130 18 18 41. 17. 43 31 43 17 43 30. 31 17. 42 40 6 6 40. 42 40 6. 42. 120. lag 10 lag 11 lag 12. 100 120 140 160 180 200. > (beer,lags=12, ). 100 120 140 160 180 200 100 120 140 160 180 200. Time series and forecasting in R Basic time series functionality 11 Time series and forecasting in R Basic time series functionality 12. ACF PACF. > pacf(beer). > acf(beer). Partial ACF. ACF. ! ! ! Lag Lag Time series and forecasting in R Basic time series functionality 13 Time series and forecasting in R Basic time series functionality 14.

8 ACF/PACF Spectrum Raw periodogram > spectrum(beer). acf(x, = NULL, type = c("correlation", "covariance", "partial"), plot = TRUE, = , demean = TRUE, ..). pacf(x, , plot, , ..) spectrum ARMAacf(ar = numeric(0), ma = numeric(0), = r, pacf = FALSE). 0 1 2 3 4 5 6. frequency Time series and forecasting in R Basic time series functionality 15 Time series and forecasting in R Basic time series functionality 16. Spectrum Spectrum AR(12) spectrum 500 1000. > spectrum(beer,method="ar"). spectrum(x, .., method = c("pgram", "ar")). (x, spans = NULL, kernel, taper = , 200. pad = 0, fast = TRUE, demean = FALSE, spectrum 100.)

9 Detrend = TRUE, plot = TRUE, = , ..). 50. (x, , order = NULL, plot = TRUE, 20. = , 10. method = "yule-walker", ..). 0 1 2 3 4 5 6. frequency Time series and forecasting in R Basic time series functionality 17 Time series and forecasting in R Basic time series functionality 18. Classical decomposition STL decomposition decompose(beer) plot(stl(beer, "periodic")). Decomposition of additive time series 190. observed data 160. 160. 120. 130. seasonal 20. 146 150 154. trend 0. !20. 40. 158. seasonal trend 20. 152. 0. 146. 0 10 !20. 15. remainder random 5. !5. !20. !15. 1991 1992 1993 1994 1995 1991 1992 1993 1994 1995.

10 Time time Time series and forecasting in R Basic time series functionality 19 Time series and forecasting in R The forecast package 21. Decomposition forecast package > forecast(beer). Point Forecast Lo 80 Hi 80 Lo 95 Hi 95. decompose(x, type = c("additive", "multiplicative"), Sep 1995 filter = NULL) Oct 1995 Nov 1995 stl(x, , = 0, Dec 1995 Jan 1996 = NULL, = 1, Feb 1996 = nextodd(period), = , Mar 1996 = ceiling( ), Apr 1996 = ceiling( ), May 1996 = ceiling( ), Jun 1996 robust = FALSE, Jul 1996 Aug 1996 inner = if(robust) 1 else 2, Sep 1996 outer = if(robust) 15 else 0, Oct 1996 = ) Nov 1996 Dec 1996 Jan 1997 Feb 1997 Mar 1997 Apr 1997 May 1997 Time series and forecasting in R The forecast package 22 Time series and forecasting in R The forecast package 23.