Forecasting

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Forecasting Volatility

The paper compares the forecasting ability of the most popular volatility forecasting models and develops an alternative. The comparison of existing models focuses on four issues: 1) the relative weighting of recent versus older observations, 2) the estimation criteria, 3) the trade-off in terms of out-of-sample forecasting error between simple and complex models, and 4) the emphasis placed on large shocks. Like previous studies, we find that financial markets have longer memories than reflected in GARCH(1,1) model estimates but find this has little impact on out-of-sample forecasting ability. While more complex models which allow a more flexible weighting pattern than the exponential model forecast better on an in-sample basis, due to the additional estimation error introduced by additional parameters, they forecast poorly out-of-sample. With the exception of GARCH models, we find that models based on absolute return deviations generally forecast volatility better than otherwise equivalent models based on squared return deviations. Among the most popular time series models, we find that GARCH(1,1) generally yields better forecasts than the historical standard deviation and exponentially weighted moving average models though between GARCH and EGARCH there is no clear favorite. However, in terms of forecast accuracy, all are dominated by a new, simple, non-linear least squares model, based on historical absolute return deviations, that we develop and test here.


Analysis of Financial Time-Series Using Fourier and Wavelet Methods

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This paper presents a set of tools, which allow gathering information about the frequency components of a time-series. We focus on the concepts rather than giving too much weight to mathematical technicalities.

In a first step, we discuss spectral analysis and filtering methods. Spectral analysis can be used to identify and to quantify the different frequency components of a data series. Filters permit to capture specific components (e.g. trends, cycles, seasonalities) of the original time-series. Both spectral analysis and standard filtering methods have two main drawbacks: (i) they impose strong restrictions regarding the possible processes underlying the dynamics of the series (e.g. stationarity), and, (ii) they lead to a pure frequency-domain representation of the data, i.e. all information from the time-domain representation is lost in the operation.

In a second step, we introduce wavelets, which are relatively new tools in economics and finance. They take their roots from filtering methods and Fourier analysis. But they overcome most of the limitations of these two methods. Indeed their principal advantages are the following: (1) they combine information from both time-domain and frequency-domain and, (2) they are also very flexible and do not make strong assumptions concerning the data generating process for the series under investigation.

Non-Linear Forecasting Methods: Some Applications to the Analysis of Financial Series

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The evolution of financial data shows a high degree of volatility of the series, coupled with increasing difficulties of forecasting the shorter is the time horizon, when using standard (i.e., based on linear models) forecasting methods. Some alternative forecasting methods for non-linear time series, based on the literature on complex dynamic systems, have been recently developed, which can be particularly useful in the analysis of financial time series. In this paper we present a summary of some of these new techniques, and then show some applications to the analysis of several financial series (i.e., exchange rates, stock prices, and interest rates), which illustrate the usefulness of the approach. Since non-linear forecasting methods require the usage of very long time series, the availability of high-frequency data for these variables make them the best candidates among economic time series for the application of this methodology.

A Simple Approximation of Intraday Spreads Using Daily Data

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This study examines the relation between the bid-ask spread from the daily CRSP data and the bid-ask spread from the intraday TAQ data. We show that the CRSP-based spread is highly correlated with the TAQ-based spread across stocks using data from 1993 through 2009. The simple CRSP-based spread provides a better approximation of the TAQ-based spread than all other low-frequency liquidity measures in cross-sectional settings. However, the CRSP-based spread is highly correlated with the TAQ spread in time-series settings only for NASDAQ stocks. Overall, our results suggest that the simple CRSP-based spread could be used in lieu of the TAQ-based spread in academic research that focuses on cross-sectional analysis.

Exploring Irregular Time Series Through Non-Uniform Fast Fourier Transform

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One of the fundamental shortcoming of the popular analysis tools for time series is that they require the data to be taken at uniform time intervals. However, the real-world time series, such as those from financial markets, are mostly from irregular time intervals. It is a common practice to resample the irregular time series into a regular one, but, there are significant limitations on this practice. For example, if one is to resample the trading activities on a stock into hourly series, then the time series can only last through the trading day because there usually is no trading in the night. In this work, we directly explore the dynamics of irregular time series through a tool known as Non-Uniform Fast Fourier Transform (NUFFT). To illustrate its effectiveness, we apply NUFFT on the trading records of natural gas futures contracts for the last seven years. Results accurately capture well-known structural features in the trading records, such as weekly and daily cycles, and at the same time also reveal unknown or unexplored features, such as the presence of multiple power laws. In particular, we observe a new power law in the Fourier spectra in recent years.


The Three-Pass Regression Filter: A New Approach to Forecasting Using Many Predictors

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We forecast a single time series using many predictor variables with a new estimator called the three-pass regression filter (3PRF). It is calculated in closed form and conveniently represented as a set of ordinary least squares regressions. 3PRF forecasts converge to the infeasible best forecast when both the time dimension and cross section dimension become large. This requires only specifying the number of relevant factors driving the forecast target, regardless of the total number of common (and potentially irrelevant) factors driving the cross section of predictors. We derive inferential theory in the form of limiting distributions for estimated relevant factors, predictive coefficients and forecasts, and provide consistent standard error estimators. We explore two empirical applications that exemplify the many predictor problem: Forecasting macroeconomic aggregates with a large panel of economic indices, and forecasting stock market aggregates with many individual assets' price-dividend ratios. These, combined with a range of Monte Carlo experiments, demonstrate the 3PRF's forecasting power.

Forecasting Time Series Subject to Multiple Structural Breaks

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This paper provides a novel approach to forecasting time series subject to discrete structural breaks. We propose a Bayesian estimation and prediction procedure that allows for the possibility of new breaks over the forecast horizon, taking account of the size and duration of past breaks (if any) by means of a hierarchical hidden Markov chain model. Predictions are formed by integrating over the hyper parameters from the meta distributions that characterize the stochastic break point process. In an application to US Treasury bill rates, we find that the method leads to better out-of-sample forecasts than alternative methods that ignore breaks, particularly at long horizons.

MS_Regress : The MATLAB Package for Markov Regime Switching Models

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Markov state switching models are a type of specification which allows for the transition of states as an intrinsic property of the econometric model. Such type of statistical representations are well known and utilized in different problems in the field of economics and finance. This paper gives an overview of MS_Regress, a Matlab toolbox specially designed for the estimation, simulation and forecasting of a general markov regime switching model. The package was written in an intuitive manner so that the user have at its reach a large number of different markov switching specifications, without any change in the original code. This document introduces the main functionality of the package with the help of several empirical examples.

A Model for the Federal Funds Rate Target

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This paper is a statistical analysis of the manner in which the Federal Reserve determines the level of the Federal funds rate target, one of the most publicized and anticipated economic indicators in the financial world. The analysis presents two econometric challenges: (1) changes in the target are irregularly spaced in time; (2) the target is changed in discrete increments of 25 basis points. The contributions of this paper are: (1) to give a detailed account of the changing role of the target in the conduct of monetary policy; (2) to develop new econometric tools for analyzing time-series duration data; (3) to analyze empirically the determinants of the target. The paper introduces a new class of models termed autoregressive conditional hazard processes, which allow one to produce dynamic forecasts of the probability of a target change. Conditional on a target change, an ordered probit model produces predictions on the magnitude by which the Fed will raise or lower the Federal funds rate. By decomposing Federal funds rate innovations into target changes and nonchanges, we arrive at new estimates of the effects of a monetary policy "shock."

GARCH 101: An Introduction to the Use of Arch/Garch Models in Applied Econometrics

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ARCH and GARCH models have become important tools in the analysis of time series data, particularly in financial applications. These models are especially useful when the goal of the study is to analyze and forecastvolatility. This paper gives the motivation behind the simplest GARCH model and illustrates its usefulness in examining portfolio risk. Extensions are briefly discussed.


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