Forecast comparison of principal component regression and principal covariate regression

Forecasting with many predictors is of interest, for instance, inmacroeconomics and finance. This paper compares two methods for dealing withmany predictors, that is, principal component regression (PCR) and principalcovariate regression (PCovR). Theforecast performance of these methods is compared by simulating data fromfactor models and from regression models. The simulations show that, in general, PCR performs better for the first type of data and PCovR performs better for the second type of data. The simulations also clarify the effect of the choice of the PCovR weight on the orecast quality.economic forecasting;principal components;factor model;principal covariates;regression model

Forecast comparison of principal component regression and principal covariate regression

Forecasting with many predictors is of interest, for instance, in macroeconomics and finance. This paper compares two methods for dealing with many predictors, that is, principal component regression (PCR) and principal covariate regression (PCovR). The forecast performance of these methods is compared by simulating data from factor models and from regression models. The simulations show that, in general, PCR performs better for the first type of data and PCovR performs better for the second type of data. The simulations also clarify the effect of the choice of the PCovR weight on the orecast quality

Improved forecasting with leading indicators: the principal covariate index

We propose a new method of leading index construction that combines the need for data compression with the objective of forecasting. This so-called principal covariate index is constructed to forecast growth rates of the Composite CoincidentIndex. The forecast performance is compared with an alternative index based on principal components and with the Composite Leading Index of the Conference Board. The results show that the new index, which takes the forecast objective explicitly into account, provides significant gains over other single-index methods, both in terms of forecast accuracy and in terms of predicting recession probabilities.business cycles;turning points;index construction;principal covariate;principal component;time series forecasting

Time series forecasting by principal covariate regression.

This paper is concerned with time series forecasting in the presence of a large numberof predictors. The results are of interest, for instance, in macroeconomic and financialforecasting where often many potential predictor variables are available. Most of thecurrent forecast methods with many predictors consist of two steps, where the largeset of predictors is first summarized by means of a limited number of factors -forinstance, principal components- and, in a second step, these factors and their lags areused for forecasting. A possible disadvantage of these methods is that the constructionof the components in the first step is not directly related to their use in forecasting inthe second step. This motivates an alternative method, principal covariate regression(PCovR), where the two steps are combined in a single criterion. This method hasbeen analyzed before within the framework of multivariate regression models. Moti-vated by the needs of macroeconomic time series forecasting, this paper discusses twoadjustments of standard PCovR that are necessary to allow for lagged factors and forpreferential predictors. The resulting nonlinear estimation problem is solved by meansof a method based on iterative majorization. The paper discusses some numericalaspects and analyzes the method by means of simulations. Further, the empirical per-formance of PCovR is compared with that of the two-step principal component methodby applying both methods to forecast four US macroeconomic time series from a set of132 predictors, using the data set of Stock and Watson (2005).distributed lags;dynamic factor models;economic forecasting;iterative majorization;principal components;principal covariate regression

High-Frequency Principal Components and Evolution of Liquidity in a Limit Order Market

The paper applies a popular methodology of competing risks to the analysis of the timing and interaction between the Deutsche Mark/U.S. dollar transactions, quotes, and cancellations in the Reuters D2000-2 electronic brokerage system. Consistently with previous stock market studies, the bid-ask spread and market depth at the best bid and ask quotes are found to be major determinants of limit order market dynamics at ultra-high frequencies. Consistently with the microstructure approach to exchange rate determination, the signed transaction activity appears to be the main factor behind the limit order market dynamics at lower frequencies. Application of principal component analysis to the covariate indices of competing risks identifies five pervasive factors that capture 85% of the Reuters D2000-2 limit order book activity. The multifactor competing risks model substantially improves the quality of short-term probability forecasts for buyer- and seller initiated transactions, relative to popular moving average-type forecasting rulesforeign exchange, limit order, market order, order flow, liquidity, competing risks, principal component, probability forecast

Forecasting age-specific breast cancer mortality using functional data models

Accurate estimates of future age-specific incidence and mortality are critical for allocation of resources to breast cancer control programs and evaluation of screening programs. The purpose of this study is to apply functional data analysis techniques to model age-specific breast cancer mortality time trends, and forecast entire age-specific mortality function using a state-space approach. We use yearly unadjusted breast cancer mortality rates in Australia, from 1921 to 2001 in 5 year age groups (45 to 85+). We use functional data analysis techniques where mortality and incidence are modeled as curves with age as a functional covariate varying by time. Data is smoothed using nonparametric smoothing methods then decomposed (using principal components analysis) to estimate basis functions that represent the functional curve. Period effects from the fitted functions are forecast then multiplied by the basis functions, resulting in a forecast mortality curve with prediction intervals. To forecast, we adopt a state-space approach and an extension of the Pegels modeling framework for selecting among exponential smoothing methods. Overall, breast cancer mortality rates in Australia remained relatively stable from 1960 to the late 1990's but declined over the last few years. A set of K=4 basis functions minimized the mean integrated squared forecasting error (MISFE) and accounts for 99.3% of variation around the mean mortality curve. 20 year forecast suggest a continual decline at a slower rate and stabilize beyond 2010 and by age, forecasts show a decline in all age groups with the greatest decline in older women. We illustrate the utility of a new modelling and forecasting approach to model breast cancer mortality rates using a functional model of age. The methods have the potential to incorporate important covariates such as Hormone Replacement Therapy (HRT) and interventions to represent mammographic screening. This would be particularly useful for evaluating the impact of screening on mortality and incidence from breast cancer.Mortality, Breast Cancer, Forecasting, Functional Data Analysis, Exponential Smoothing

Forecasting the Yield Curve in a Data-Rich Environment using the Factor-Augmented Nelson-Siegel Model

Various ways of extracting macroeconomic information from a data-rich environment are compared with the objective of forecasting yield curves using the Nelson-Siegel model. Five issues in factor extraction are addressed, namely, selection of a subset of the available information, incorporation of the forecast objective in constructing factors, specification of a multivariate forecast objective, data grouping before constructing factors, and selection of the number of factors in a data-driven way. Our empirical results show that each of these features helps to improve forecast accuracy, especially for the shortest and longest maturities. The data-driven methods perform well in relatively volatile periods, when simpler models do not suffice

Forecasting Quarter-on-Quarter Changes of German GDP with Monthly Business Tendency Survey Results

Results from business tendency surveys are often used to construct leading indicators. The indicators are then, for example, employed to forecast GDP growth. In this article more detailed results of business tendency surveys are used to forecast quarter-onquarter GDP growth. The target series is very challenging because this type of growth rate leads to quite volatile time series. The present study focuses on German GDP data and survey results provided by the Ifo Institute. Since numerous time series of possible indicators result from the surveys, methods that can handle this setting are applied. One candidate method is principal component analysis, which is used to reduce dimensionality. On the other hand, subset selection procedures are applied. For the present setting the latter method seems more successful than principal components. But this is not a statement about the two types of procedures in general. Which method should be favoured depends very much on the aims of the specific study.Business tendency surveys, business cycle analysis, principal component regression, subset selection.