Practical estimation from the sum of ar(1) processes

Ku, Simon; Seneta, E.

doi:10.1080/03610919808813521

Cited by 8 publications

(3 citation statements)

References 6 publications

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“…This paper shows that aggregating across second (or first)‐order (integrated) moving average processes leads to an aggregate process whose parameters are direct functions of the micro processes. That is, no iteration procedure is needed to recover the parameters of the aggregate process provided that the data generation process is known (similar results relative to the aggregation of first‐order moving average processes have been achieved by Ku and Seneta, , and Sbrana and Silvestrini, , ). Those results are shown in the next section, which considers the aggregation of both independent and dependent processes.…”

Section: Introductionmentioning

confidence: 70%

Forecasting Aggregated Moving Average Processes with an Application to the Euro Area Real Interest Rate

Sbrana

2011

Journal of Forecasting

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This paper focuses on the contemporaneous aggregation of moving average processes. It is shown that aggregating across second (or first)-order (integrated) moving average processes leads to a macro process whose parameters are exact functions of the parameters of its generation process. Similar results are obtained at single equation level when a vector moving average framework is considered. In addition, the out-of-sample forecasting properties of aggregate and disaggregate procedures to forecast the aggregate variable are provided. Moreover, it is shown that the condition of equality of aggregate and disaggregate predictors is not necessary for the equality of their mean squared errors. Finally, an application to the euro area real interest rate is presented and discussed.

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Section: Introductionmentioning

confidence: 70%

Forecasting Aggregated Moving Average Processes with an Application to the Euro Area Real Interest Rate

Sbrana

2011

Journal of Forecasting

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“… See Lütkepohl (1987, p. 102).6 This expression was previously used byKu and Seneta (1998) to show the relation between the parameters of two independent AR(1) processes and those of the sum process.…”

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confidence: 97%

Comparing aggregate and disaggregate forecasts of first order moving average models

Sbrana

Silvestrini

2010

Stat Papers

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This paper compares the performance of "aggregate" and "disaggregate" predictors in forecasting contemporaneously aggregated vector MA(1) processes. The necessary and sufficient condition for the equality of mean squared errors associated with the two competing predictors is provided in the bivariate MA(1) case. Furthermore, it is argued that the condition of equality of predictors as stated by Lütkepohl (Forecasting aggregated vector ARMA processes, Springer, Berlin, 1987) is only sufficient (not necessary) for the equality of mean squared errors. Finally, it is shown that the equality of forecasting accuracy for the two predictors can be achieved using specific assumptions on the parameters of the vector MA(1) structure.

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“…There is certainly a line-of-descent on estimation theory for m in branching processes with immigration, which is traced in Section 1 of Qi (2007). A related line of descent, which also continues, can be traced from Ku and Seneta (1998).…”

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confidence: 99%

Chris Heyde on Branching Processes and Population Genetics

Seneta

2010

Selected Works of C.C. Heyde

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this commentary. A strong impetus to branching process theory had occurred with the appearance of the book of Harris (1963).The dominant theme of Chris's work prior to his arrival had been refinement of classical limit theory for sums of independent random variables. A principal theme of his work since 1970 has been the theory and use of martingale methods in situations of statistical dependence. This seems to have its origin in his paper [M31], in the context of a simple (Bienaymé-Galton-Watson) branching process {Z n }, n ³ 0; Z 0 = 1. Suppose the non-degenerate offspring distribution has probability generating function< ∞ the process is called supercritical, and in this case the probability of extinction, q, is the unique real number in [0, 1) satisfying F(q) = q. The random sequence {Z n ∕ m n } is clearly a non-negative martingale, which in the supercritical case under the-then standard condition 2 1( ) E Z < ∞ was known to converge almost surely (a.s) to a random variable W for which P(W = 0) = q and which has a continuous density on the set of positive real numbers. After a number of refinements of this convergence result, it was shown in Seneta (1968) that in the non-degenerate supercitical case without further conditions, the choice c n = 1 ∕ h n (s 0 ), where s 0 is any fixed number in (0, − logq), and h n (s 0 ) is the n-th functional iterate of h(s), which is the inverse function of k(s) = − log F (e − s ), results in convergence in distribution of {Z n ∕ c n } to a proper non-degenerate random variable, W. While it was noticed that {W n = h n (s 0 )Z n } was a submartingale, a.s. convergence could not be deduced from the usual theorem since E(W n ) is bounded if and only if E(Z 1 logZ 1 ) < ∞. Chris's insight was that {exp ( − h n (s 0 )Z n )} is a martingale, with (obviously) bounded mean, thus giving the sharpening to a.s. convergence. Reciprocally, this strengthening immediately led to an analogous result for the supercritical branching process with immigration {X n } (Seneta, 1970)

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Practical estimation from the sum of ar(1) processes

Cited by 8 publications

References 6 publications

Forecasting Aggregated Moving Average Processes with an Application to the Euro Area Real Interest Rate

Forecasting Aggregated Moving Average Processes with an Application to the Euro Area Real Interest Rate

Comparing aggregate and disaggregate forecasts of first order moving average models

Chris Heyde on Branching Processes and Population Genetics

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