Structural breaks and long memory in US inflation rates: do they matter for forecasting?

There is substantial evidence that several economic time series variables experience occasional structural breaks. At the same time, for some of these variables there is evidence of long memory. In particular, it seems that inflation rates have both features. One cause for this finding may be that the two features are difficul

Asymmetries, breaks, and long-range dependence: An estimation framework for daily realized volatility

We study the simultaneous occurrence of long memory and nonlinear effects, such as structural breaks and thresholds, in autoregressive moving average (ARMA) time series models and apply our modeling framework to series of daily realized volatility. Asymptotic theory for the quasi-maximum likelihood estimator is developed and a sequence of model specification tests is described. Our framework allows for general nonlinear functions, including smoothly changing intercepts. The theoretical results in the paper can be applied to any series with long memory and nonlinearity. We apply the methodology to realized volatility of individual stocks of the Dow Jones Industrial Average during the period 1995 to 2005. We find strong evidence of nonlinear effects and explore different specifications of the model framework. A forecasting exercise demonstrates that allowing for nonlinearities in long memory models yields significant performance gains.Realized volatility, structural breaks, smooth transitions, nonlinear models, long memory, persistence.

Terms of Trade and Supply Response of Indian Agriculture: Analysis in Cointegration Framework.

In this paper, we examine the presence of stochastic trend (unit root) and structural break in various agriculture-industry terms of trade series in India. The results suggest that underlying data generating process of terms of trade are most likely non-stationary. We subsequently re-examine the aggregate supply response of Indian agriculture in this light. We investigate the presence of long-run functional relationship(s) underlying the supply response model through cointegration analysis and error correction framework. The multivariate results indicate presence of a cointegrating relationship in the supply response model. The vector error correction estimates suggest that short-run output adjustments are not related to changes in agricultural terms of trade in a temporal causal relationship. However, the short-run deviations in terms of trade from its long-term level create error-correction in the long-term output adjustments through changes in technology (irrigation). This may imply that agricultural growth can respond better if price incentives are combined with investments in irrigation.domestic terms of trade, agricultural supply response, unit root, cointegration

Long memory estimation of stochastic volatility for index prices

One of the typical ways of measuring risk associated with persistence in financial data set can be done through studies of long memory and volatility. Finance is a branch of economics concerned with resource allocation which deals with money, time and risk and their interrelation. The investors invest at risk over a period of time for the opportunity to gain profit. Since the last decade, the complex issues of long memory and short memory confounded with occasional structural break had received extensive attention. Structural breaks in time series can generate a strong persistence and showing a slower rate of decay in the autocorrelation function which is an observed behaviour of a long memory process. Besides that, the persistence in volatility cannot be captured easily because some of the mathematical models are not able to detect these properties. To overcome these drawbacks, this study developed a procedure to construct long memory stochastic volatility (LMSV) model by using fractional Ornstein-Uhlenbeck (fOU) process in financial time series to evaluate the degree of the persistence property of the data. The drift and volatility parameters of the fractional Ornstein-Unlenbeck model are estimated separately using least square estimator (LSE) and quadratic generalized variations (QGV) method respectively. Whereas, the long memory parameter namely Hurst parameter is estimated by using several heuristic methods and a semi-parametric method. The procedure of constructing LMSV model and the estimation methods are applied to the real daily index prices of FTSE Bursa Malaysia KLCI over a period of 20 years. The findings showed that the volatility of the index prices exhibit long memory process but the returns of the index prices do not show strong persistence properties. The root mean square errors (RMSE) obtained from various methods indicates that the performances of the model and estimators in describing returns of the index prices are good

Empirical analysis of the dynamics of the South African rand (Post-1994)

Thesis (Ph.D. (Economics))--University of the Witwatersrand, Faculty of Commerce, Law and Management, School of Economic & Business Sciences, 2016.The objective of this thesis is to investigate the recent historical dynamics of the four major nominal bilateral spot foreign exchange rates and the fifteen currency-basket nominal effective exchange rate of the South African rand (hereafter referred to as the rand). The thesis has been organised as three separate studies that add to the advancement of the knowledge of the characteristics and behaviour (causal effects) of the rand. The common thread that holds the individual chapters together is the study of the dynamics of the rand. In particular, the study establishes whether the apparent nonstationarity of the exchange rate is a product of unit root test misspecification (a failure to account for structural change), considers the connexions between the timing of the identified structural shifts and important economic and noneconomic events, and analyses rand volatility and the temporal effect of monetary policy surprises on both the spot foreign exchange market returns and volatility of the rand. In order to do this, low- and high-frequency data are employed. With regard to exchange rate modelling, the theoretical economic-exchange rate frameworks are approached both from the traditional macro-based view of exchange rate determination and a micro-based perspective. The various methodologies applied here tackle different aspects of the exchange rate dynamics. To preview the results, we find that adjusting for structural shifts in the unit root tests does not render any of the exchange rates stationary. However, the results show a remarkable fall in the estimates of volatility persistence when structural breaks are integrated into the autoregressive conditional heteroskedasticity (ARCH) framework. The empirical results also shed light on the impact of modelling exchange rates as long memory processes, the extent of asymmetric responses to ‘good news’ and ‘bad news’, the consistencies and contrasts in the five exchange rate series’ volatility dynamics, and the timing and likely triggers of volatility regime switching. Additionally, there are convincing links between the timing of structural changes and important economic (and noneconomic) events, and commonality in the structural breaks detected in the levels and volatility of the rand. We also find statistically and economically significant high-frequency exchange rate returns and volatility responses to domestic interest rate surprises. Furthermore, the rapid response of the rand to monetary policy surprises suggests a relatively high degree of market efficiency (from a mechanical perspective) in processing this information. Keywords: Exchange rate, expectations, long memory, monetary policy surprises, repo rate, structural breaks, volatility; unit root. JEL Code: C22, E52, E58, F31, F41, G14 and G1

Diffusive hidden Markov model characterization of DNA looping dynamics in tethered particle experiments

In many biochemical processes, proteins bound to DNA at distant sites are brought into close proximity by loops in the underlying DNA. For example, the function of some gene-regulatory proteins depends on such DNA looping interactions. We present a new technique for characterizing the kinetics of loop formation in vitro, as observed using the tethered particle method, and apply it to experimental data on looping induced by lambda repressor. Our method uses a modified (diffusive) hidden Markov analysis that directly incorporates the Brownian motion of the observed tethered bead. We compare looping lifetimes found with our method (which we find are consistent over a range of sampling frequencies) to those obtained via the traditional threshold-crossing analysis (which can vary depending on how the raw data are filtered in the time domain). Our method does not involve any time filtering and can detect sudden changes in looping behavior. For example, we show how our method can identify transitions between long-lived, kinetically distinct states that would otherwise be difficult to discern

Inflation and monetary dynamics in the US: a Quantity-Theory Approach

In this paper we investigate the long-run link between inflation and money growth in the US since 1960. A measure of the long-run inflation trend is constructed, which bears the interpreation of "monetary" inflation rate and is directly related to the excess nominal money growth process (money growth less output growth) as postulated by the quantity theory. Consistent with the memory characteristics of the series, their fractional integration and cointegration properties are taken into account in empirical modelling. The proposed measure is then compared with several existing measures of "core inflation'', aimed at capturing long-run inflation dynamics but unrelated to money growth. The "monetary'' long-run inflation rate performs well in out-of-sample forecasting exercises especially over a two- to three-year horizon, yielding valuable information to monetary policymakers

Essays on fractional cointegration and long memory time series

This dissertation contains three essays on distinguishing between structural breaks under long memory, testing for fractional cointegration relationship between the financial markets and developing optimal forecast methods under long memory in the presence of a discrete structural break. Chapter 1 introduces the concepts of long memory, fractional cointegration and briefly describes the rest of the chapters. Chapter 2 suggests a testing procedure to discriminate between stationarity, a break in the mean and a break in persistence in a time series that may exhibit long memory is introduced. The asymptotic properties of test statistics based on the CUSUM statistic are studied. In a Monte Carlo study we further analyze the finite sample properties of the procedure. An application to inflation rates shows the potential of our procedure for future research. Chapter 3 revisits the question whether volatilities of different markets and trading zones have a long-run equilibrium in the sense that they are fractionally cointegrated. We consider the U.S., Japanese and German stock, bond and foreign exchange markets to see whether there is fractional cointegration between the markets in one trading zone or for one market across trading zones. Also the other combinations of different markets in different trading zones are considered. Applying a purely semiparametric approach through the whole analysis shows fractional cointegration can only be found for a small minority of different cases. Investigating further we find that all volatility series show persistence breaks during the observation period which may be a reason for different findings in previous studies. Finally, we develop methods in Chapter 4 to obtain optimal forecast under long memory in the presence of a discrete structural break based on different weighting schemes for the observations. We observe significant changes in the forecasts when long-range dependence is taken into account. Using Monte Carlo simulations, we confirm that our methods substantially improve the forecasting performance under long memory. We further present an empirical application to inflation rates that emphasizes the importance of our methods