Time-series analysis supported by power transformations (original) (raw)
Related papers
Variance Stabilizing Power Transformation for Time Series
Journal of Modern Applied Statistical Methods, 2004
A confidence interval was derived for the index of a power transformation that stabilizes the variance of a time-series. The process starts from a model-independent procedure that minimizes a coefficient of variation to yield a point estimate of the transformation index. The confidence coefficient of the interval is calibrated through a simulation.
On the Use of the Power Transformation Models to Improve the Temperature Time Series
Statistics, Optimization & Information Computing
The aim of this paper is to select an appropriate ARIMA model for the time series after transforming the original responses. Box-Cox and Yeo-Johnson power transformation models were used on the response variables of two time series datasets of average temperatures and then diagnosed and built the appropriate ARIMA models for each time-series. The authors treat the results of the model fitting as a package in an attempt to decide and choose the best model by diagnosing the effect of the data transformation on the response normality, significant of estimated model parameters, forecastability and the behavior of the residuals. The authors conclude that the Yeo-Johnson model was more flexible in smoothing the data and contributedto accessing a simple model with good forecastability.
Journal of Modern Applied Statistical Methods, 2010
Selected data transformation techniques in time series modeling are evaluated using real-life data on Botswana Gross Domestic Product (GDP). The transformation techniques considered were modified, although reasonable estimates of the original with no significant difference at 0.05 α = level were obtained: minimizing square of first difference (MFD) and minimizing square of second difference (MSD) provided the best transformation for GDP, whereas the Goldstein and Khan (GKM) method had a deficiency of losing data points. The Box-Jenkins procedure was adapted to fit suitable ARIMA (p, d, q) models to both the original and transformed series, with AIC and SIC as model order criteria. ARIMA (3, 1, 0) and ARIMA (1, 0, 0) were identified, respectively, to the original and log of the transformed series. All estimates of the fitted stationary series were significant and provided a reliable forecast.
Wavelet Transform as an Alternative to Power Transformation in Time Series Analysis
Bulletin of Mathematical Sciences and Applications, 2016
This study examines the discrete wavelet transform as a transformation technique in the analysis of non-stationary time series while comparing it with power transformation. A test for constant variance and choice of appropriate transformation is made using Bartlett’s test for constant variance while the Daubechies 4 (D4) Maximal Overlap Discrete Wavelet Transform (DWT) is used for wavelet transform. The stationarity of the transformed (power and wavelet) series is examined with Augmented Dickey-Fuller Unit Root Test (ADF). The stationary series is modeled with Autoregressive Moving Average (ARMA) Model technique. The model precision in terms of goodness of fit is ascertained using information criteria (AIC, BIC and SBC) while the forecast performance is evaluated with RMSE, MAD, and MAPE. The study data are the Nigeria Exchange Rate (2004-2014) and the Nigeria External Reserve (1995-2010). The results of the analysis show that the power transformed series of the exchange rate data a...
Nonstationary time series transformation methods: An experimental review
Knowledge-Based Systems, 2018
Data preprocessing is a crucial step for mining and learning from data, and one of its primary activities is the transformation of data. This activity is very important in the context of time series prediction since most time series models assume the property of stationarity, i.e., statistical properties do not change over time, which in practice is the exception and not the rule in most real datasets. There are several transformation methods designed to treat nonstationarity in time series. However, the choice of a transformation that is appropriate to the adopted data model and to the problem at hand is not a simple task. This paper provides a review and experimental analysis of methods for transformation of nonstationary time series. The focus of this work is to provide a background on the subject and a discussion on their advantages and limitations to the problem of time series prediction. A subset of the reviewed transformation methods is compared through an experimental evaluation using benchmark datasets from time series prediction competitions and other real macroeconomic datasets. Suitable nonstationary time series transformation methods provided improvements of more than 30% in prediction accuracy for half of the evaluated time series and improved the prediction in more than 95% for 10% of the time series. Furthermore, the adoption of a validation phase during model training enables the selection of suitable transformation methods.
A New Approach of Power Transformations in Functional Non-Parametric Temperature Time Series
Time Series Analysis - New Insights [Working Title]
In nonparametric analyses, many authors indicate that the kernel density functions work well when the variable is close to the Gaussian shape. This chapter interest is on the improvement the forecastability of the functional nonparametric time series by using a new approach of the parametric power transformation. The choice of the power parameter in this approach is based on minimizing the mean integrated square error of kernel estimation. Many authors have used this criterion in estimating density under the assumption that the original data follow a known probability distribution. In this chapter, the authors assumed that the original data were of unknown distribution and set the theoretical framework to derive a criterion for estimating the power parameter and proposed an application algorithm in two-time series of temperature monthly averages.
Using Transformations to Predict and Smooth Time Series
2021
Time series has a leading position in statistical Analysis. Nowadays, many economic and industrial operations have been built based on time series. These operations include predicting the product demand variation, the future product prices oscillation, the stock storing control etc. This paper presents a study to show the effect of transformation and smoothing on the performance of the time series. The research results have shown a significant improvement in time-series operation can be noticed when the principles of transformation and smoothing are applied on time series. Introduction Time series topic is one of the essential topics nowadays because it is starting to be applied to different types of science widely. Mathematical-statistical possesses in analyzing the time series have begun to provide important functions of estimation. Furthermore, other involved significant points have made important decisions, and they used to simulate some mathematics and statistics samples for th...
Identifying and Overcoming Transformation Bias in Forecasting Models
2022
Log and square root transformations of target variable are routinely used in forecasting models to predict future sales. These transformations often lead to better performing models. However, they also introduce a systematic negative bias (under-forecasting). In this paper, we demonstrate the existence of this bias, dive deep into its root cause and introduce two methods to correct for the bias. We conclude that the proposed bias correction methods improve model performance (by up to 50%) and make a case for incorporating bias correction in modeling workflow. We also experiment with 'Tweedie' family of cost functions which circumvents the transformation bias issue by modeling directly on sales. We conclude that Tweedie regression gives the best performance so far when modeling on sales making it a strong alternative to working with a transformed target variable.
Data transformation and forecasting in models with unit roots and cointegration
2001
We perform a series of Monte Carlo experiments in order to evaluate the impact of data transformation on forecasting models, and¯nd that vector error-corrections dominate di®erenced data vector autoregressions when the correct data transformation is used, but not when data are incorrectly tansformed, even if the true model contains cointegrating restrictions. We argue that one reason for this is the failure of standard unit root and cointegration tests under incorrect data transformation.