Error correction in DHSY

In this note, we consider the contradiction between the fact that the best fit for the UK consumption data in Davidson et al. (1978) is obtained using an equation with an intercept but without an error correction term, whereas the equation with error correction and without the intercept has better post-sample forecasting properties than the former equation. This contradiction is explained and the two equations reconciled in a nonlinear framework by applying a smooth transition regression model to the data.consumption equation; model misspecification testing; nonlinearity; smooth transition regression

Using CAViaR models with implied volatility for value-at-risk estimation

This paper proposes VaR estimation methods that are a synthesis of conditional autoregressive value at risk (CAViaR) time series models and implied volatility. The appeal of this proposal is that it merges information from the historical time series and the different information supplied by the market’s expectation of risk. Forecast combining methods, with weights estimated using quantile regression, are considered. We also investigate plugging implied volatility into the CAViaR models, a procedure that has not been considered in the VaR area so far. Results for daily index returns indicate that the newly proposed methods are comparable or superior to individual methods, such as the standard CAViaR models and quantiles constructed from implied volatility and the empirical distribution of standardised residual. We find that the implied volatility has more explanatory power as the focus moves further out into the left tail of the conditional distribution of S&P500 daily returns

Principal component analysis for second-order stationary vector time series

We extend the principal component analysis (PCA) to second-order stationary vector time series in the sense that we seek for a contemporaneous linear transformation for a $p$-variate time series such that the transformed series is segmented into several lower-dimensional subseries, and those subseries are uncorrelated with each other both contemporaneously and serially. Therefore those lower-dimensional series can be analysed separately as far as the linear dynamic structure is concerned. Technically it boils down to an eigenanalysis for a positive definite matrix. When $p$ is large, an additional step is required to perform a permutation in terms of either maximum cross-correlations or FDR based on multiple tests. The asymptotic theory is established for both fixed $p$ and diverging $p$ when the sample size $n$ tends to infinity. Numerical experiments with both simulated and real data sets indicate that the proposed method is an effective initial step in analysing multiple time series data, which leads to substantial dimension reduction in modelling and forecasting high-dimensional linear dynamical structures. Unlike PCA for independent data, there is no guarantee that the required linear transformation exists. When it does not, the proposed method provides an approximate segmentation which leads to the advantages in, for example, forecasting for future values. The method can also be adapted to segment multiple volatility processes.Comment: The original title dated back to October 2014 is "Segmenting Multiple Time Series by Contemporaneous Linear Transformation: PCA for Time Series

Non-Cointegration and Econometric Evaluation of Models of Regional Shift and Share

This paper tests for cointegration between regional output of an industry and national output of the same industry. An equilibrium economic theory is presented to argue for the plausibility of cointegration, however, regional economic forecasting using the shift and share framework often acts as if cointegration does not exist. Data analysis on broad industrial sectors for 20 states finds very little evidence for cointegration. Forecasting models with and without imposing cointegration are than constructed and used to forecast out of sample. The simplest, non-cointegrating models are the best.

Forecasting Intraday Time Series with Multiple Seasonal Cycles Using Parsimonious Seasonal Exponential Smoothing

This paper concerns the forecasting of seasonal intraday time series. An extension of Holt-Winters exponential smoothing has been proposed that smoothes an intraday cycle and an intraweek cycle. A recently proposed exponential smoothing method involves smoothing a different intraday cycle for each distinct type of day of the week. Similar days are allocated identical intraday cycles. A limitation is that the method allows only whole days to be treated as identical. We introduce an exponential smoothing formulation that allows parts of different days of the week to be treated as identical. The result is a method that involves the smoothing and initialisation of fewer terms than the other two exponential smoothing methods. We evaluate forecasting up to a day ahead using two empirical studies. For electricity load data, the new method compares well with a range of alternatives. The second study involves a series of arrivals at a call centre that is open for a shorter duration at the weekends than on weekdays. By contrast with the previously proposed exponential smoothing methods, our new method can model in a straightforward way this situation, where the number of periods on each day of the week is not the same.Exponential smoothing; Intraday data; Electricity load; Call centre arrivals.

Forecasting Time-Series with Correlated Seasonality

A new approach is proposed for forecasting a time series with multiple seasonal patterns. A state space model is developed for the series using the single source of error approach which enables us to develop explicit models for both additive and multiplicative seasonality. Parameter estimates may be obtained using methods adapted from general exponential smoothing, although the Kalman filter may also be used. The proposed model is used to examine hourly and daily patterns in hourly data for both utility loads and traffic flows. Our formulation provides a model for several existing seasonal methods and also provides new options, which result in superior forecasting performance over a range of prediction horizons. The approach is likely to be useful in a wide range of applications involving both high and low frequency data, and it handles missing values in a straightforward manner.Exponential smoothing; Holt-Winters; Seasonality; Structural time series model

Forecasting time series with complex seasonal patterns using exponential smoothing

A new innovations state space modeling framework, incorporating Box-Cox transformations, Fourier series with time varying coefficients and ARMA error correction, is introduced for forecasting complex seasonal time series that cannot be handled using existing forecasting models. Such complex time series include time series with multiple seasonal periods, high frequency seasonality, non-integer seasonality and dual-calendar effects. Our new modelling framework provides an alternative to existing exponential smoothing models, and is shown to have many advantages. The methods for initialization and estimation, including likelihood evaluation, are presented, and analytical expressions for point forecasts and interval predictions under the assumption of Gaussian errors are derived, leading to a simple, comprehensible approach to forecasting complex seasonal time series. Our trigonometric formulation is also presented as a means of decomposing complex seasonal time series, which cannot be decomposed using any of the existing decomposition methods. The approach is useful in a broad range of applications, and we illustrate its versatility in three empirical studies where it demonstrates excellent forecasting performance over a range of prediction horizons. In addition, we show that our trigonometric decomposition leads to the identification and extraction of seasonal components, which are otherwise not apparent in the time series plot itself.Exponential smoothing, Fourier series, prediction intervals, seasonality, state space models, time series decomposition

Forecasting with Micro Panels: The Case of Health Care Costs

Copyright © 2016 John Wiley & Sons, Ltd. Micro panels characterized by large numbers of individuals observed over a short time period provide a rich source of information, but as yet there is only limited experience in using such data for forecasting. Existing simulation evidence supports the use of a fixed-effects approach when forecasting but it is not based on a truly micro panel set-up. In this study, we exploit the linkage of a representative survey of more than 250,000 Australians aged 45 and over to 4 years of hospital, medical and pharmaceutical records. The availability of panel health cost data allows the use of predictors based on fixed-effects estimates designed to guard against possible omitted variable biases associated with unobservable individual specific effects. We demonstrate the preference towards fixed-effects-based predictors is unlikely to hold in many practical situations, including our models of health care costs. Simulation evidence with a micro panel set-up adds support and additional insights to the results obtained in the application. These results are supportive of the use of the ordinary least squares predictor in a wide range of circumstances. Copyright © 2016 John Wiley & Sons, Ltd

Higher wages for relief work can make many of the poor worse off : recent evidence from Maharashtra's"Employment Guarantee Scheme"

Among developing countries, the"Employment Guarantee Scheme"(EGS) in the state of Maharashtra in India is probably the most famous and most successful direct governmental effort at reducing absolute poverty in rural areas. Since the mid-1970s, EGS has aimed to offer unskilled rural employment on demand. The work creates or maintains rural infrastructure, through small scale irrigation and soil conservation projects, re-forestation, and rural road building. EGS projects are designed to be highly intensive in their use of unskilled labor, which typically accounts for over two-thirds of variable costs. Wages are set in the form of piece rates, stipulating rates of pay for a large number of specific tasks, such asdigging, breaking rocks, shifting earth, and transplanting. This paper investigates the effects on the scheme of the dramatic change in the EGS wage schedule in mid-1988. Three issues are addressed: (a) EGS employment, wage rates, and the cost of the scheme to the government after the increase in the statutory minimum wage rate; (b) the determinants of EGS employment and changes incurred by the wage increase; and (c) the availability of local employment at the going EGS wages.Rural Poverty Reduction,Safety Nets and Transfers,Environmental Economics&Policies,Banks&Banking Reform,Services&Transfers to Poor