Ondaietas e previsão de séries de tempo: uma análise empírica

This paper presents three case studies in time series forecasting. We try to compare the use of traditional ARIMA models with an alternative method that combines of ARIMA and Wavelets models. Two different approaches are applied. In the first one, Wavelets are used to fraction the original time series, so that ARIMA forecasting is performed on the ffactioned series. The fractioned forecasting is then jointed to obtain the original series forecasting. The second alternative method consist in using Wavelets to smooth the original series before using traditional ARIMA forecasting

Using wavelets for time series forecasting: Does it pay off?

By means of wavelet transform a time series can be decomposed into a time dependent sum of frequency components. As a result we are able to capture seasonalities with time-varying period and intensity, which nourishes the belief that incorporating the wavelet transform in existing forecasting methods can improve their quality. The article aims to verify this by comparing the power of classical and wavelet based techniques on the basis of four time series, each of them having individual characteristics. We find that wavelets do improve the forecasting quality. Depending on the data's characteristics and on the forecasting horizon we either favour a denoising step plus an ARIMA forecast or an multiscale wavelet decomposition plus an ARIMA forecast for each of the frequency components. --Forecasting,Wavelets,ARIMA,Denoising,Multiscale Analysis

About the role of monetary aggregates for monetary policy: the case of Peru

The purpose of this paper is to analyze the relevance of monetary aggregates for monetary policy as indicators of real activity. The main hypothesis of this paper is that narrow monetary aggregates can help forecasting real output. The empirical analysis combines the time scale decomposition of time series using wavelets and the possible existence of cointegrating relationships between money, output and prices. Using recent Peruvian data, evidence is found to support the proposed hypothesis. In particular, the results suggest the existence of co-integration between non-stationary series built using wavelet filtering. In this context, exogeneity tests reveal that narrow monetary aggregates are weakly and strongly exogenous; i.e., they are helpful for forecasting real output. These results suggest that money has a role for monetary policy as an indicador of real activity.

Filtering and Forecasting Spot Electricity Prices in the Increasingly Deregulated Australian Electricity Market

Modelling and forecasting the volatile spot pricing process for electricity presents a number of challenges. For increasingly deregulated electricity markets, like that in the Australian state of New South Wales, there is need to price a range of derivative securities used for hedging. Any derivative pricing model that hopes to capture the pricing dynamics within this market must be able to cope with the extreme volatility of the observed spot prices. By applying wavelet analysis, we examine both the price and demand series at different time locations and levels of resolution to reveal and differentiate what is signal and what is noise. Further, we cleanse the data of leakage from the high frequency, mean reverting price spikes into the more fundamental levels of frequency resolution. As it is from these levels that we base the reconstruction of our filtered series, we need to ensure they are least contaminated by noise. Using the filtered data, we explore time series models as possible candidates for explaining the pricing process and evaluate their forecasting ability. These models include one from the threshold autoregressive (AR) model. What we find is that models from the TAR class produce forecasts that best appear to capture the mean and variance components of the actual data.electricity; wavelets, time series models; forecasting

Detecting patterns in Time Series Data with applications in Official Statistics

This thesis examines the issue of detecting components or features within time series data in automatic procedures. We begin by introducing the concept of Wavelets and briefly show their usage as a tool for detection. This leads to our first contribution which is a novel method using wavelets for identifying correlation structures in time series data which are often ambiguous with very different contexts. Using the properties of the wavelet transform we show the ability to distinguish between short memory models with changepoints and long memory models. The next two Chapters consider seasonality within data, which is often present in time series used in Offical Statistics. We first describe the historical evolution of identification of seasonality, comparing and contrasting methodology as it has expanded throughout time. Following this, motivated by the increased use of high-frequency time series in Official Statistics and a lack of methods for identifying low-frequency seasonal components within high-frequency data, we present a method for identifying periodicity in a series with the use of a simple wavelet decomposition. Presented with theoretical results and simulations, we show how the seasonality of a series is uniquely represented within a wavelet transform and use this to identify low frequency components which are often overlooked in favour of a trend, with very different interpretations. Finally, beginning with the motivation of forecasting European Area GDP at the current time point, we show the effectiveness of an algorithm which detects the most useful data and structures for a Dynamic Factor Model. We show its effectiveness in reducing forecasting errors but show that under large scale simulation that the recovery of the true structure over two dimensions is a difficult task. All the chapters of this thesis are motivated by, and give applications to, time series from different areas of Official Statistics

Innovative Second-Generation Wavelets Construction With Recurrent Neural Networks for Solar Radiation Forecasting

Solar radiation prediction is an important challenge for the electrical engineer because it is used to estimate the power developed by commercial photovoltaic modules. This paper deals with the problem of solar radiation prediction based on observed meteorological data. A 2-day forecast is obtained by using novel wavelet recurrent neural networks (WRNNs). In fact, these WRNNS are used to exploit the correlation between solar radiation and timescale-related variations of wind speed, humidity, and temperature. The input to the selected WRNN is provided by timescale-related bands of wavelet coefficients obtained from meteorological time series. The experimental setup available at the University of Catania, Italy, provided this information. The novelty of this approach is that the proposed WRNN performs the prediction in the wavelet domain and, in addition, also performs the inverse wavelet transform, giving the predicted signal as output. The obtained simulation results show a very low root-mean-square error compared to the results of the solar radiation prediction approaches obtained by hybrid neural networks reported in the recent literature

Modeling and forecasting exchange rate volatility in time-frequency domain

This paper proposes an enhanced approach to modeling and forecasting volatility using high frequency data. Using a forecasting model based on Realized GARCH with multiple time-frequency decomposed realized volatility measures, we study the influence of different timescales on volatility forecasts. The decomposition of volatility into several timescales approximates the behaviour of traders at corresponding investment horizons. The proposed methodology is moreover able to account for impact of jumps due to a recently proposed jump wavelet two scale realized volatility estimator. We propose a realized Jump-GARCH models estimated in two versions using maximum likelihood as well as observation-driven estimation framework of generalized autoregressive score. We compare forecasts using several popular realized volatility measures on foreign exchange rate futures data covering the recent financial crisis. Our results indicate that disentangling jump variation from the integrated variation is important for forecasting performance. An interesting insight into the volatility process is also provided by its multiscale decomposition. We find that most of the information for future volatility comes from high frequency part of the spectra representing very short investment horizons. Our newly proposed models outperform statistically the popular as well conventional models in both one-day and multi-period-ahead forecasting

A Wavelet Approach for Factor-Augmented Forecasting

It has been acknowledged that wavelets can constitute a useful tool for forecasting in economics. Through a wavelet multiresolution analysis, a time series can be decomposed into different time-scale components and a model can be fitted to each component to improve the forecast accuracy of the series as a whole. Up to now, the literature on forecasting with wavelets has mainly focused on univariate modelling. On the other hand, in a context of growing data availability, a line of research has emerged on forecasting with large datasets. In particular, the use of factor-augmented models have become quite widespread in the literature and among practitioners. The aim of this paper is to bridge the two strands of the literature. A wavelet approach for factor-augmented forecasting is proposed and put to test for forecasting GDP growth for the major euro area countries. The results show that the forecasting performance is enhanced when wavelets and factor-augmented models are used together.