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From |
"Clarence" <johnsnowjr@yahoo.co.uk> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: Help with ARIMA |

Date |
Thu, 24 Apr 2003 13:53:58 -0000 |

Thanks for the detailed explanation! This seems to work. Although if I use the 'condition' option, I still have the same problem (matsize being too small) when I try to make out-of-sample forecasts. 'diffuse' works OK, if slowly, as advised. C. --- In statalist@yahoogroups.com, vwiggins@s... (Vince Wiggins, StataCorp) wrote: > Clarence Tam <Clarence.Tam@l...> asks whether he needs to have Stata/SE > to estimate an arima model with an MA term at the 52nd lag, > > > [...] Model diagnostics suggest that there's a residual seasonal > > correlation (at week 52) both in the ACF and PACF. My next step was > > going to be to include an additional AR or MA term to account for > > this, but I'm not sure how to do it. I've tried: > > > > . arima DS52.lnreps, ar(1) ma(1 52) noconstant > > > > but Stata says that the matsize is too small, even though it's set > > at the maximum of 800 (I'm using Intercooled Stata 8.0). > > Does anyone have any suggestions on how to get round this problem > > (preferably ones that don't involve upgrading to Stata SE...)? > > > Answer > ------ > > Clarence does not need to upgrade to SE. > > The message he received after his -arima- command should have been, > > matsize too small, must be max(AR, MA+1)^2 > use -diffuse- option or type -help matsize- > > In this case, with the maximum MA being 52, the message implies that a matrix > size of 53^2=2809 is required, and that would indeed require Stata/SE. The > first suggestion in the message, however, will let him use Intercooled Stata > to estimate the model. If Clarence types, > > . arima DS52.lnreps, ar(1) ma(1 52) noconstant diffuse > ^^^^^^^ > he should be able to estimate the model. > > > Explanation > ----------- > > By default -arima- uses a Kalman filter to produce unconditional maximum > likelihood estimates of the specified model. To obtain the unconditional > estimates the Kalman filter must be initialized with the expected value of the > initial state vector and the MSE of this vector. These initial values depend > on the current parameter estimates and in computing the MSE we must invert a > square matrix the size of the state vector -- max(AR, MA+1)^2. Thus, the need > for such a large matrix. These are the most efficient estimates for the model > because the initial state vector and its MSE are forced to conform to the > current parameter estimates. > > We can, however, obtain slightly less efficient estimates by assuming that the > initial state vector is zero and its variance is unknown and effectively > infinite. This is what the -diffuse- option specifies. This assumption > essential down-weights the initial observations until the data itself can be > used to develop a state vector and its MSE. > > With large datasets, the two estimates tend to be close. > > > Suggestion > ---------- > > Even though this model has only 4 parameters, including sigma, the Kalman > filter iterations may be somewhat slow because the filter must maintain a > state vector that is the maximum of the largest AR or MA term and will thus be > flopping around some pretty large matrices to compute the likelihood at each > observation. For this reason, I would recommend that Clarence use the > -condition- option to estimate the model, > > . arima DS52.lnreps, ar(1) ma(1 52) noconstant condition > ^^^^^^^^^ > > The -condition- option specifies conditional-maximum likelihood estimates, > rather than unconditional. These estimates to not require maintaining a state > vector. Specifically, all pre-sample values of the white noise, e_t, and > autocorrelated, u_t, disturbances are taken to be 0 and the MSE of e_t is > taken to be constant over the entire sample. Effectively this means that the > initial observations in the sample get just as much weight as the middle or > end observations even though we know less about them. We know less because > the process is autocorrelated and this implies that knowing the past > observations tells us something about the current observation, and because > nothing is known about the pre-sample observations. > > What unconditional maximum likelihood effectively does is use the current > estimates to imply information about the pre-sample while optimally > down-weighting this information so that the initial observations get a little > less weight that the remaining observations. > > What the -diffuse- option effectively does is to say we know nothing about the > pre-sample and accordingly down-weights the initial observations in the sample > even more. > > What conditional maximum likelihood effectively does is assume that the > pre-sample values are their long-run expected value of zero, that we know this > just as well as we know later later, and accordingly weights the initial > observations equally with the remaining observations. > > With large datasets, it generally does not matter which method we use because > the contribution of the initial observations is dominated by the remaining > data. Note, however, that "large" must be used carefully when the process has > large autocorrelation terms. > > > > -- Vince > vwiggins@s... > > * > * For searches and help try: > * http://www.stata.com/support/faqs/res/findit.html > * http://www.stata.com/support/statalist/faq > * http://www.ats.ucla.edu/stat/stata/ * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**References**:**Re: st: Help with ARIMA***From:*vwiggins@stata.com (Vince Wiggins, StataCorp)

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