Inflation, forecast intervals and long memory regression models

Abstract

We examine recursive out-of-sample forecasting of monthly postwar U.S. core inflation and log price levels. We use the autoregressive fractionally integrated moving average model with explanatory variables (ARFIMAX). Our analysis suggests a significant explanatory power of leading indicators associated with macroeconomic activity and monetary conditions for forecasting horizons up to two years. Even after correcting for the effect of explanatory variables, there is conclusive evidence of both fractional integration and structural breaks in the mean and variance of inflation in the 1970s and 1980s and we incorporate these breaks in the forecasting model for the 1980s and 1990s. We compare the results of the fractionally integrated ARFIMA(0,d,0) model with those for ARIMA(1,d,1) models with fixed order of d = 0 and d = 1 for inflation. Comparing mean squared forecast errors, we find that the ARMA(1,1) model performs worse than the other models over our evaluation period 1984-1999. The ARIMA(1,1,1) model provides the best forecasts, but its multi-step forecast intervals are too large.

Forecasting daily variability of the S&P 100 stock index using historical, realised and implied volatility measurements

“…However, the estimation is not without hurdles. It is, for example, pointed out by Brodsky and Hurvich (1999) and Bos, Franses, and Ooms (2002) that standard ARMA(1, 1) models can also capture long memory features and that, depending on the sample spectrum of the data, not all parameters of an ARFIMA(1,d,1) can be empirically identified from the data. This typically applies to the case of realised volatility.…”

Modelagem de séries temporais financeiras: uma abordagem estatística para a identificação de modelos de média condicional

“…Para a hipótese nula do teste ser rejeitada e a subsérie ser considerada estacionária esta deve satisfazer a desigualdade (9), tendo como valor crítico tabelado DF crit = −2, 58 uma vez que N = 500 e o nível de significância desejado, de 1%. Desta forma, de acordo com os resultados dos coeficientes descritos na Tabela I, constatou-se a não-estacionariedade de ambas as subséries, sendo uma diferenciação destes dados o suficiente para atender à desigualdade (9). Logo, atesta-se para o uso da estrutura I de ordem d = 1 na composição da subclasse de modelo para a descrição destes segmentos.…”

“…Atualmente, diversos autores utilizam ainda estes modelos em estruturas multivariadas, capazes de modelar simultaneamente mais de uma variável endógena do processo e sua interdependência, conforme aplicado por Öller em [8]. Somente uma parcela menor dos trabalhos leva em consideração influências exógenas no modelo do processo, como usado por Bos et al [9], através do modelo autorregressivo integrador de média móvel com entrada exógena (do inglês autoregressive integrated moving-average, ARIMAX). Este último propicia, entre os modelos de média condicional, representações mais fidedignas da dinâmica do preço/retorno de ativos em decorrência de fatores externos, como valores de mercados internacionais e, portanto, também será objeto de estudo neste trabalho.…”

A structural common factor approach to core inflation estimation and forecasting

“…According to the results of the Monte Carlo analysis reported in the Appendix, the estimator of Robinson (1998) 16 has been employed in the analysis. In addition to be unbiased, the estimator is the one characterised by minimum RMSE, relative to the Local Whittle estimator (Kunsch, 1987;Robinson, 1995b), the log periodogram estimator (Geweke and Porter Hudak, 1983;Robinson, 1995), and the averaged periodogram estimator (Robinson, 1994;Lobato and Robinson, 1996)).…”

“…1 The core inflation process proposed by Morana (2002), therefore, is derived from the estimation of a structural model for inflation, granting a theoretical definition to the core inflation process in terms of monetary inflation rate. 2 Coherent with recent contributions in the literature, which point to the presence of long memory and structural change in inflation (see for instance Hassler and Wolters, 1995; Baillie et al, 1996;Delgado and Robinson, 1994;Bos et al, 1999Bos et al, , 2001; Ooms and Doornik, 1999;Morana, 2000Morana, , 2002 Hyung and Franses, 2001; Baum et al, 2001), a more accurate modelling of the persistence properties of core inflation is also allowed in this framework. 1 In Bagliano and Morana (2003a,b) nominal money growth and inflation are modelled as I(1) processes and the quantity theory relationship involves only the nominal money rate of growth and the inflation rate, being output growth assumed to be I(0).…”