Hi,
I am trying to understand SARIMA models a bit better.
Data below -
Assuming no MA term (for simplicity), I know we can replicate the output of the SARIMA commands with OLS commands.
However, when I add AR1 term in SARIMA as well (#P argument), can we match the output with an OLS specification as well?
I am not sure how to match the output, and would appreciate any help here.
I am trying to understand SARIMA models a bit better.
Data below -
Code:
* Example generated by -dataex-. For more info, type help dataex clear input int air float time int t float(lnair month year) 112 1949 1 4.7184987 1 1949 118 1949.0834 2 4.770685 2 1949 132 1949.1666 3 4.882802 3 1949 129 1949.25 4 4.859812 4 1949 121 1949.3334 5 4.795791 5 1949 135 1949.4166 6 4.905275 6 1949 148 1949.5 7 4.997212 7 1949 148 1949.5834 8 4.997212 8 1949 136 1949.6666 9 4.912655 9 1949 119 1949.75 10 4.779123 10 1949 104 1949.8334 11 4.644391 11 1949 118 1949.9166 12 4.770685 12 1949 115 1950 13 4.744932 1 1950 126 1950.0834 14 4.836282 2 1950 141 1950.1666 15 4.94876 3 1950 135 1950.25 16 4.905275 4 1950 125 1950.3334 17 4.828314 5 1950 149 1950.4166 18 5.003946 6 1950 170 1950.5 19 5.135798 7 1950 170 1950.5834 20 5.135798 8 1950 158 1950.6666 21 5.062595 9 1950 133 1950.75 22 4.890349 10 1950 114 1950.8334 23 4.7361984 11 1950 140 1950.9166 24 4.941642 12 1950 145 1951 25 4.976734 1 1951 150 1951.0834 26 5.010635 2 1951 178 1951.1666 27 5.181784 3 1951 163 1951.25 28 5.09375 4 1951 172 1951.3334 29 5.147494 5 1951 178 1951.4166 30 5.181784 6 1951 199 1951.5 31 5.293305 7 1951 199 1951.5834 32 5.293305 8 1951 184 1951.6666 33 5.214936 9 1951 162 1951.75 34 5.087596 10 1951 146 1951.8334 35 4.983607 11 1951 166 1951.9166 36 5.111988 12 1951 171 1952 37 5.141664 1 1952 180 1952.0834 38 5.192957 2 1952 193 1952.1666 39 5.26269 3 1952 181 1952.25 40 5.198497 4 1952 183 1952.3334 41 5.209486 5 1952 218 1952.4166 42 5.384495 6 1952 230 1952.5 43 5.438079 7 1952 242 1952.5834 44 5.488938 8 1952 209 1952.6666 45 5.342334 9 1952 191 1952.75 46 5.252274 10 1952 172 1952.8334 47 5.147494 11 1952 194 1952.9166 48 5.267858 12 1952 196 1953 49 5.278115 1 1953 196 1953.0834 50 5.278115 2 1953 236 1953.1666 51 5.463832 3 1953 235 1953.25 52 5.459586 4 1953 229 1953.3334 53 5.433722 5 1953 243 1953.4166 54 5.493062 6 1953 264 1953.5 55 5.575949 7 1953 272 1953.5834 56 5.605802 8 1953 237 1953.6666 57 5.46806 9 1953 211 1953.75 58 5.351858 10 1953 180 1953.8334 59 5.192957 11 1953 201 1953.9166 60 5.303305 12 1953 204 1954 61 5.31812 1 1954 188 1954.0834 62 5.236442 2 1954 235 1954.1666 63 5.459586 3 1954 227 1954.25 64 5.42495 4 1954 234 1954.3334 65 5.455321 5 1954 264 1954.4166 66 5.575949 6 1954 302 1954.5 67 5.710427 7 1954 293 1954.5834 68 5.680172 8 1954 259 1954.6666 69 5.556828 9 1954 229 1954.75 70 5.433722 10 1954 203 1954.8334 71 5.313206 11 1954 229 1954.9166 72 5.433722 12 1954 242 1955 73 5.488938 1 1955 233 1955.0834 74 5.451038 2 1955 267 1955.1666 75 5.587249 3 1955 269 1955.25 76 5.594711 4 1955 270 1955.3334 77 5.598422 5 1955 315 1955.4166 78 5.752573 6 1955 364 1955.5 79 5.897154 7 1955 347 1955.5834 80 5.849325 8 1955 312 1955.6666 81 5.743003 9 1955 274 1955.75 82 5.613128 10 1955 237 1955.8334 83 5.46806 11 1955 278 1955.9166 84 5.627621 12 1955 284 1956 85 5.648974 1 1956 277 1956.0834 86 5.624018 2 1956 317 1956.1666 87 5.758902 3 1956 313 1956.25 88 5.746203 4 1956 318 1956.3334 89 5.762052 5 1956 374 1956.4166 90 5.924256 6 1956 413 1956.5 91 6.023448 7 1956 405 1956.5834 92 6.003887 8 1956 355 1956.6666 93 5.872118 9 1956 306 1956.75 94 5.723585 10 1956 271 1956.8334 95 5.602119 11 1956 306 1956.9166 96 5.723585 12 1956 315 1957 97 5.752573 1 1957 301 1957.0834 98 5.70711 2 1957 356 1957.1666 99 5.874931 3 1957 348 1957.25 100 5.852202 4 1957 end
Assuming no MA term (for simplicity), I know we can replicate the output of the SARIMA commands with OLS commands.
Code:
//SARIMA * arima(#p,#d,#q) specify ARIMA(p,d,q) model for dependent variable * sarima(#P,#D,#Q,#s) specify period-#s multiplicative seasonal ARIMA term arima lnair, arima(2,1,0) sarima(0,0,0,12) //OLS reg D.lnair L1.D.lnair L2.D.lnair i.year
However, when I add AR1 term in SARIMA as well (#P argument), can we match the output with an OLS specification as well?
Code:
//SARIMA arima lnair, arima(2,1,0) sarima(1,0,0,12) //OLS ???
