In this paper, we analyze the possible confusion in terms of long memory behavior of the autocorrelation function of a Markov switching model. Such a model is known to have a short memory behavior. Analyzing the value of sum of the transition probabilities and the number of switches inside such a model, we show their impact to create long memory. The ability of the true Markov switching model to predict is compared with the forecasts obtained from a long memory process adjusted on data derived from the former model. It is shown that, in certain cases, this spurious long memory behavior can be benefit to get better forecasts.

It is well know that long memory can be caused by regime switching and is easily confused with it. However, recent study suggests that if the cause of confusion were properly controlled for, long memory and regime switching could be distinguished. Motivated by this idea, our study aims to distinguish Regime Switching from Long Memory for the financial time series. In this paper, we model long memory and regime switching via the ARFIMA and Markov Regime-Switching (MRS) frameworks respectively. A theoretical proof is provided to show that the time-varying smoothing probability series can induce the presence of significant long memory in the regime switching process. We then propose a two-stage Two-State-ARFIMA (2S-ARFIMA) model to control for the effect of the smoothing probability and use a simulation study to demonstrate that it can effectively distinguish the pure MRS process from the pure ARFIMA process.

The theoretical and empirical econometric literatures on long memory and regime switching have evolved largely independently, as the phenomena appear distinct. We argue, in contrast, that they are intimately related, and we substantiate our claim in several environments, including a simple mixture model, Engle and Lee's (1999) stochastic permanent break model, and Hamilton's (1989) Markov switching model. In particular, we show analytically that stochastic regime switching is easily confused with long memory, even asymptotically, so long as only a small' amount of regime switching occurs, in a sense that we make precise. A Monte Carlo analysis supports the relevance of the theory and produces additional insights.

When applied to time series processes containing occasional level shifts, the log-periodogram (GPH) estimator often finds long memory. For a stationary markov switching process, which does not contain long memory, I show that the GPH estimator is substantially biased and I derive an asymptotic approximation to this bias. The asymptotic bias lies on the (0,1) interval with the exact value depending on the ratio of the expected number of breaks to a user-defined bandwidth parameter. I also examine the bias in the GPH estimator when applied to a nonstationary hidden markov breaks process and the stochastic permanent breaks process.

This paper finds the close relationship between long memory and some forms of Markov-switching models. The simulation results suggest: (1) when the transition probabilities are closer to unity, it is more likely to generate long memory process; (2) magnitude of regime-switching plays an important role in generating long memory; and (3) process with switching in variance (disturbance) is much less likely to explain long memory process than switching in mean (intercept) and autoregressive coefficient. Therefore, given the observed high persistence in financial volatility data, volatility modeling by switching in mean and AR coefficient is preferred to that by switching in variance.

Assembles three different strands of long memory analysis: statistical literature on the properties of, and tests for, LRD processes; mathematical literature on the stochastic processes involved; and models from economic theory providing plausible micro foundations for the occurrence of long memory in economics.