Indirect Inference for Locally Stationary Models

We propose the use of indirect inference estimation to conduct inference in complex locally stationary models. We develop a local indirect inference algorithm and establish the asymptotic properties of the proposed estimator. Due to the nonparametric nature of locally stationary models, the resulting indirect inference estimator exhibits nonparametric rates of convergence. We validate our methodology with simulation studies in the confines of a locally stationary moving average model and a new locally stationary multiplicative stochastic volatility model. Using this indirect inference methodology and the new locally stationary volatility model, we obtain evidence of non-linear, time-varying volatility trends for monthly returns on several Fama-French portfolios

Mean Likelihood Estimation And Time Series Analysis

In this thesis, I develop mean likelihood estimation (MeLE) and maximum likelihood estimation (MLE) for the parameters of a fractionally differenced autoregressive moving average (FARMA) model and its integrated form (IFARMA).;In chapter 1, I study the sampling distribution theory of MeLE by embedding the estimation problem into a Bayesian model.;In chapter 2, I apply MeLE and MLE to the estimation of the moving average parameter of a MA(1) model. The main result is that the MeLE has a smaller mean square error than the MLE when the moving average parameter is sufficiently inside the parameter space. I also demonstrate that the concentrated likelihood function of a time series with a MA(1) component has a local maximum or minimum at the boundary {dollar}\pm{dollar}1.;In chapter 3, I give the theory and methods needed to simulate FARMA series and to estimate the parameters of the FARMA model by MeLE and MLE. I explain how to calculate the exact value of the likelihood function for the parameters of a FARMA model. I show how to integrate functions over the stationary and invertible region of an ARMA process. Finally, I conduct simulation studies that compare the MLE and MeLE in combination with various algorithms to calculate them.;In the last chapter, I solve the problem of defining a likelihood function that unifies both the stationary FARMA and non-stationary IFARMA models, and I show how to select an appropriate model for a given time series by using a minimum information criteria strategy

Integer-valued time series and renewal processes

This research proposes a new but simple model for stationary time series of integer counts. Previous work in the area has focused on mixture and thinning methods and links to classical time series autoregressive moving-average difference equations; in contrast, our methods use a renewal process to generate a correlated sequence of Bernoulli trials. By superpositioning independent copies of such processes, stationary series with binomial, Poisson, geometric, or any other discrete marginal distribution can be readily constructed. The model class proposed is parsimonious, non-Markov, and readily generates series with either short or long memory autocovariances. The model can be fitted with linear prediction techniques for stationary series. Estimation of process parameters based on conditional least squares methods is considered. Asymptotic properties of the estimators are derived. The models sometimes have an autoregressive moving-average structure and we consider the AR(1) count process case in detail. Unlike previous methods based on mixture and thinning tactics, series with negative autocorrelations can be produced

Fully modified least absolute devotions and fully modified M in estimating regression model with non-stationary explanatory variable and auto correlated random errors

The research is concerned with the adoption of two robust estimation methods: The fully modified least absolute devotions method (FM-LAD) and the fully modified M method (FM-M), in estimating the parameters of regression model with non-stationary explanatory variable and autocorrelated random errors which can be modeled according to one of the mixed models, autoregressive and moving average (ARMA). The research aims to make a comparison between these two methods based on the results of their estimation using simulation experiments prepared for this purpose. The results of the simulation experiment showed the advantage of the fully modified M method over the second method depending on the trade-off criterion mean squared error (MSE)

A note on state-space representations of locally stationary wavelet time series

In this note we show that the locally stationary wavelet process can be decomposed into a sum of signals, each of which follows a moving average process with time-varying parameters. We then show that such moving average processes are equivalent to state space models with stochastic design components. Using a simple simulation step, we propose a heuristic method of estimating the above state space models and then we apply the methodology to foreign exchange rates data

A geostatistical model based on Brownian motion to Krige regions in R2 with irregular boundaries and holes

Master's Project (M.S.) University of Alaska Fairbanks, 2019Kriging is a geostatistical interpolation method that produces predictions and prediction intervals. Classical kriging models use Euclidean (straight line) distance when modeling spatial autocorrelation. However, for estuaries, inlets, and bays, shortest-in-water distance may capture the system’s proximity dependencies better than Euclidean distance when boundary constraints are present. Shortest-in-water distance has been used to krige such regions (Little et al., 1997; Rathbun, 1998); however, the variance-covariance matrices used in these models have not been shown to be mathematically valid. In this project, a new kriging model is developed for irregularly shaped regions in R 2 . This model incorporates the notion of flow connected distance into a valid variance-covariance matrix through the use of a random walk on a lattice, process convolutions, and the non-stationary kriging equations. The model developed in this paper is compared to existing methods of spatial prediction over irregularly shaped regions using water quality data from Puget Sound