type="main" xml:id="jtsa12054-abs-0001" <p>We present an elaboration of the usual binomial AR(1) process on {0,1, … ,N}that allows the thinning probabilities to depend on the current state N only through the ‘density’ n ∕ N, a natural assumption in many real contexts. We derive some...</p>

type="main" xml:id="jtsa12057-abs-0001"We give stable finite-order vector autoregressive moving average (p-super-   ,q-super-   ) representations for M-state Markov switching second-order stationary time series whose autocovariances satisfy a certain matrix relation. The upper bounds for...

type="main" xml:id="jtsa12081-abs-0001"A time-series model in which the signal is buried in noise that is non-Gaussian may throw up observations that, when judged by the Gaussian yardstick, are outliers. We describe an observation-driven model, based on an exponential generalized beta...

type="main" xml:id="jtsa12080-abs-0001" <title type="main">SUMMARY</title>Indirect estimators usually emerge from two-step optimization procedures. Each step in such a procedure may induce complexities in the asymptotic theory of the estimator. In this note, we are occupied with a simple example in which the estimator...

type="main" xml:id="jtsa12069-abs-0001"A frequency domain methodology is proposed for estimating parameters of covariance functions of stationary spatio-temporal processes. Finite Fourier transforms of the processes are defined at each location. Based on the joint distribution of these complex...

type="main" xml:id="jtsa12078-abs-0001"The parameters of integer autoregressive models with Poisson, or negative binomial innovations can be estimated by maximum likelihood where the prediction error decomposition, together with convolution methods, is used to write down the likelihood function....

type="main" xml:id="jtsa12058-abs-0001" <title type="main">Abstract</title>This article first studies the non-stationarity of the first-order double AR model, which is defined by the random recurrence equation <math xmlns="http://www.w3.org/1998/Math/MathML" display="block" altimg="urn:x-wiley:01439782:media:jtsa12058:jtsa12058-math-0001" wiley:location="equation/jtsa12058-math-0001.gif"><msub><mrow><mi>y</mi></ mrow><mrow><mi>t</mi></mrow></msub><mo class="MathClass-rel">=</mo><msub><mrow><mi>φ</mi></mrow><mrow><mn>0</mn>< /mrow></msub><msub><mrow><mi>y</mi></mrow><mrow><mi>t</mi><mo class="MathClass-bin">−</mo><mn>1</mn></mrow></msub><mo class="MathClass-bin">+</mo><msub><mrow><mi>η</mi></mrow><mrow><mi>t</mi>< /mrow></msub><msqrt><mrow><msub><mrow><mi>γ</mi></mrow><mrow><mn>0</mn></m row></msub><mo class="MathClass-bin">+</mo><msub><mrow><mi>α</mi></mrow><mrow><mn>0</mn>< /mrow></msub><msubsup><mrow><mi>y</mi></mrow><mrow><mi>t</mi><mo class="MathClass-bin">−</mo><mn>1</mn></mrow><mrow><mn>2</mn></mrow></msub sup></mrow></msqrt></math>, where γ₀  0, α₀ ≥ 0, and {η_t}is a sequence of i.i.d. symmetric...<//msub></msubsup><//m></mrow><//></mrow>

type="main" xml:id="jtsa12051-abs-0001"The standard state space model treats observations as imprecise measurement of the Markovian states. Our flexible model handles the states and observations symmetrically, which are simultaneously determined by past observations and up to first-lagged...

type="main" xml:id="jtsa12079-abs-0001"We discuss robust M-estimation of INARCH models for count time series. These models assume the observation at each point in time to follow a Poisson distribution conditionally on the past, with the conditional mean being a linear function of previous...