The limiting distribution of the least squares estimate of the derived process of a noninvertible and nearly noninvertible moving average model with infinite variance innovations is established as a functional of a Lévy process. The form of the limiting law depends on the initial value of the...

A mean square error criterion is proposed in this paper to provide a systematic approach to approximate a long-memory time series by a short-memory ARMA(1, 1) process. Analytic expressions are derived to assess the effect of such an approximation. These results are established not only for the...

By allowing deviations from equilibrium to follow a fractionally integrated process, the notion of fractional cointegration analysis encompasses a wide range of mean-reverting behaviors. For fractional cointegrations, asymptotic theories have been extensively studied, and numerous empirical...

Consider a structural break autoregressive (SBAR) process <disp-formula id="UM0001"> <graphic xmlns:xlink="http://www.w3.org/1999/xlink" position="float" orientation="portrait" xlink:href="uasa_a_866566_um0001.gif"/> </disp-formula>where <inline-formula> <inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="uasa_a_866566_ilm0001.gif"/> </inline-formula> <italic>j</italic> = 1, ..., <italic>m</italic> + 1, {<italic>t</italic> ₁, ..., <italic>t_m </italic>} are change-points, 1 = <italic>t</italic> ₀ <italic>t</italic> ₁ ⋅⋅⋅ <italic>t</italic> _{<italic>m</italic> + 1} = <italic>n</italic> + 1, σ( · ) is a measurable function on <inline-formula> <inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="uasa_a_866566_ilm0002.gif"/> </inline-formula>, and {ϵ_{<italic>t</italic>}} are white noise with unit variance. In practice, the number of change-points...</italic>

An empirical likelihood–based confidence interval is proposed for interval estimations of the autoregressive coefficient of a first-order autoregressive model via weighted score equations. Although the proposed weighted estimate is less efficient than the usual least squares estimate, its...

Let Xt=∑j=0∞cjεt−j be a moving average process with GARCH (1, 1) innovations {εt}. In this paper, the asymptotic behavior of the quadratic form Qn=∑j=1n∑s=1nb(t−s)XtXs is derived when the innovation {εt} is a long-memory and heavy-tailed process with tail index α, where {b(i)} is...

Recent research suggests that fractional Brownian motion can be used to model the long-range dependence structure of the stock market. Fractional Brownian motion is not a semi-martingale and arbitrage opportunities do exist, however. Hu and Øksendal [Infin. Dimens. Anal., Quant. Probab. Relat....