By Petr Mandl

ISBN-10: 0387041427

ISBN-13: 9780387041421

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04239 | | | | | | . . . " marks two standard errors . . . 04054 -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1 | ************| . | | . |**. | | . |* . | | . *| . | | . |* . 01756 | | | | | | . |**. ****| . |**** ***| . |* . | . 00962 -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1 | . **| . | | . | . | | . |* . | | . | . 03510 | | | | | | . *| . | . **| . |*** . *| . |* . 966 Number of Residuals 200 * AIC and SBC do not include log determinant. 046 The ARIMA Procedure Model for variable Y Data have been centered by subtracting the value No mean term in this model.

Then the variance of ρ (Y t −1 − µ) + e t 28 SAS for Forecasting Time Series is ρ 2 σ2 / (1 − ρ 2 ) + σ2 = σ2 1 − ρ2 ) / ( which shows that the variance of Yt is also σ 2 / (1 − ρ 2 ) . 2 back into the infinite past. This again shows that if ρ < 1 the effect of shocks in the past is minimal. 3, in which the series is expressed in terms of a mean and past shocks, is often called the “Wold representation” of the series. 3. Calling this covariance γ ( j) = c o v (Y t ,Y t − j ) you have γ ( j ) = ρ σ 2 / (1 − ρ 2 ) = ρ j j Y) var ( t An interesting feature is that γ ( j ) does not depend on t.

Furthermore, you see that the mean (expected value) of Yt is µ . Suppose the variance of Yt-1 is σ 2 / (1 − ρ 2 ) . Then the variance of ρ (Y t −1 − µ) + e t 28 SAS for Forecasting Time Series is ρ 2 σ2 / (1 − ρ 2 ) + σ2 = σ2 1 − ρ2 ) / ( which shows that the variance of Yt is also σ 2 / (1 − ρ 2 ) . 2 back into the infinite past. This again shows that if ρ < 1 the effect of shocks in the past is minimal. 3, in which the series is expressed in terms of a mean and past shocks, is often called the “Wold representation” of the series.

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Analytical Treatment of One-Dimensional Markov Processes. by Petr Mandl


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