Showing papers on "Moving-average model published in 2014"

Beta regression for time series analysis of bounded data, with application to Canada Google Flu Trends.

Abstract: Bounded time series consisting of rates or proportions are often encountered in applications. This manuscript proposes a practical approach to analyze bounded time series, through a beta regression model. The method allows the direct interpretation of the regression parameters on the original response scale, while properly accounting for the heteroskedasticity typical of bounded variables. The serial dependence is modeled by a Gaussian copula, with a correlation matrix corresponding to a stationary autoregressive and moving average process. It is shown that inference, prediction, and control can be carried out straightforwardly, with minor modifications to standard analysis of autoregressive and moving average models. The methodology is motivated by an application to the influenza-like-illness incidence estimated by the Google® Flu Trends project.

A hybrid ANFIS based on n-period moving average model to forecast TAIEX stock

Abstract: Linear model is a general forecasting model and moving average technical index (MATI) is one of useful forecasting methods to predict the future stock prices in stock markets. Therefore, individual investors, stock fund managers, and financial analysts attempt to predict price fluctuation in stock markets by either linear model or MATI. From literatures, three major drawbacks are found in many existing forecasting models. First, forecasting rules mined from some AI algorithms, such as neural networks, could be very difficult to understand. Second, statistic assumptions about variables are required for time series to generate forecasting models, which are not easily understandable by stock investors. Third, stock market investors usually make short-term decisions based on recent price fluctuations, i.e., the last one or two periods, but most time series models use only the last period of stock price. In order to overcome these drawbacks, this study proposes a hybrid forecasting model using linear model and MATI to predict stock price trends with the following four steps: (1) test the lag period of Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX) and calculate the last n -period moving average; (2) use subtractive clustering to partition technical indicator values into linguistic values based on data discretization method objectively; (3) employ fuzzy inference system (FIS) to build linguistic rules from the linguistic technical indicator dataset, and optimize the FIS parameters by adaptive network; and (4) refine the proposed model by adaptive expectation models. The proposed model is then verified by root mean squared error (RMSE), and a ten-year period of TAIEX is selected as experiment datasets. The results show that the proposed model is superior to the other forecasting models, namely Chen's model and Yu's model in terms of RMSE.

A hybrid ANFIS based on n-period moving average model to forecast TAIEX stock

Abstract: Linear model is a general forecasting model and moving average technical index (MATI) is one of useful forecasting methods to predict the future stock prices in stock markets. Therefore, individual investors, stock fund managers, and financial analysts attempt to predict price fluctuation in stock markets by either linear model or MATI. From literatures, three major drawbacks are found in many existing forecasting models. First, forecasting rules mined from some AI algorithms, such as neural networks, could be very difficult to understand. Second, statistic assumptions about variables are required for time series to generate forecasting models, which are not easily understandable by stock investors. Third, stock market investors usually make short-term decisions based on recent price fluctuations, i.e., the last one or two periods, but most time series models use only the last period of stock price. In order to overcome these drawbacks, this study proposes a hybrid forecasting model using linear model and MATI to predict stock price trends with the following four steps: (1) test the lag period of Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX) and calculate the last n -period moving average; (2) use subtractive clustering to partition technical indicator values into linguistic values based on data discretization method objectively; (3) employ fuzzy inference system (FIS) to build linguistic rules from the linguistic technical indicator dataset, and optimize the FIS parameters by adaptive network; and (4) refine the proposed model by adaptive expectation models. The proposed model is then verified by root mean squared error (RMSE), and a ten-year period of TAIEX is selected as experiment datasets. The results show that the proposed model is superior to the other forecasting models, namely Chen's model and Yu's model in terms of RMSE.

Seasonal and trend time series forecasting based on a quasi-linear autoregressive model

Abstract: We forecast the seasonal and trend time series using a quasi-linear autoregressive model.A combined genetic optimization and gradient-based optimization algorithm is applied for automatic selection of proper input variables and the model-dependent variable, and optimizing the model parameters simultaneously.The comparison results show the effectiveness of the proposed approach for the seasonal time series. Modeling and forecasting seasonal and trend time series is an important research topic in many areas of industrial and economic activity. In this study, we forecast the seasonal and trend time series using a quasi-linear autoregressive model. This quasi-linear autoregressive model belongs to a class of varying coefficient models in which its autoregressive coefficients are constructed by radial basis function networks. A combined genetic optimization and gradient-based optimization algorithm is applied for automatic selection of proper input variables and model-dependent variables, and optimizing the model parameters simultaneously. The model is tested by five monthly time series. We compare the results with those of other various methods, which show the effectiveness of the proposed approach for the seasonal time series.

Beta regression for time series analysis of bounded data, with application to Canada Google${}^\circledR$ Flu Trends

Abstract: Bounded time series consisting of rates or proportions are often encountered in applications. This manuscript proposes a practical approach to analyze bounded time series, through a beta regression model. The method allows the direct interpretation of the regression parameters on the original response scale, while properly accounting for the heteroskedasticity typical of bounded variables. The serial dependence is modeled by a Gaussian copula, with a correlation matrix corresponding to a stationary autoregressive and moving average process. It is shown that inference, prediction, and control can be carried out straightforwardly, with minor modifications to standard analysis of autoregressive and moving average models. The methodology is motivated by an application to the influenza-like-illness incidence estimated by the Google${}^\circledR$ Flu Trends project.

Short-term traffic-flow forecasting with auto-regressive moving average models

Abstract: Short-term traffic-flow forecasting, the process of predicting future traffic conditions based on historical and real-time observations, is an essential aspect of intelligent transportation systems. The existing well-known algorithms used for short-term traffic flow include time-series analysis-based techniques, of which the seasonal auto-regressive moving average model is one of the most precise methods used in this field. The effectiveness of short-term traffic flow in an urban transport network can be fully realised only in its multivariate form where traffic flow is predicted at multiple sites simultaneously. In this paper, this concept in explored utilising an additive seasonal vector auto-regressive moving average model to predict traffic flow in the short-term future considering the spatial dependency among multiple sites. The dynamic linear model representation of the auto-regressive moving average model is used to reduce the number of latent variables. The parameters of the model are estimated in...

Optimal Formulations for Nonlinear Autoregressive Processes

Abstract: We develop optimal formulations for nonlinear autoregressive models by representing them as linear autoregressive models with time-varying temporal dependence coefficients. We propose a parameter updating scheme based on the score of the predictive likelihood function at each time point. The resulting time-varying autoregressive model is formulated as a nonlinear autoregressive model and is compared with threshold and smooth-transition autoregressive models. We establish the information theoretic optimality of the score driven nonlinear autoregressive process and the asymptotic theory for maximum likelihood parameter estimation. The performance of our model in extracting the time-varying or the nonlinear dependence for finite samples is studied in a Monte Carlo exercise. In our empirical study we present the in-sample and out-of-sample performances of our model for a weekly time series of unemployment insurance claims.

A Hybrid Time-delay Prediction Method for Networked Control System

Abstract: This paper presents an Ethernet based hybrid method for predicting random time-delay in the networked control system. First, db3 wavelet is used to decompose and reconstruct time-delay sequence, and the approximation component and detail components of time-delay sequences are figured out. Next, one step prediction of time-delay is obtained through echo state network (ESN) model and auto-regressive integrated moving average model (ARIMA) according to the different characteristics of approximate component and detail components. Then, the final predictive value of time-delay is obtained by summation. Meanwhile, the parameters of echo state network is optimized by genetic algorithm. The simulation results indicate that higher accuracy can be achieved through this prediction method.

A L\'evy-driven rainfall model with applications to futures pricing

Abstract: We propose a parsimonious stochastic model for characterising the distributional and temporal properties of rainfall. The model is based on an integrated Ornstein-Uhlenbeck process driven by the Hougaard L\'evy process. We derive properties of this process and propose an extended model which generalises the Ornstein-Uhlenbeck process to the class of continuous-time ARMA (CARMA) processes. The model is illustrated by fitting it to empirical rainfall data on both daily and hourly time scales. It is shown that the model is sufficiently flexible to capture important features of the rainfall process across locations and time scales. Finally we study an application to the pricing of rainfall derivatives which introduces the market price of risk via the Esscher transform. We first give a result specifying the risk-neutral expectation of a general moving average process. Then we illustrate the pricing method by calculating futures prices based on empirical daily rainfall data, where the rainfall process is specified by our model.

Moving average process underlying the holographic-optical-tweezers experiments.

Abstract: We study the statistical properties of recordings that contain time-dependent positions of a bead trapped in optical tweezers. Analysis of such a time series indicates that the commonly accepted model, i.e., the autoregressive process of first-order, is not sufficient to fit the data. We show the presence of a first-order moving average part in the dynamical model of the system. We explain the origin of this part as an influence of the high-frequency CCD camera on the measurements. We show that this influence evidently depends on the applied exposure time. The proposed autoregressive moving average model appears to reflect perfectly all statistical features of the high-frequency recording data.

Manual choice reaction times in the rate-domain

Abstract: Over the last 150 years, human manual reaction times (RTs) have been recorded countless times. Yet, our understanding of them remains remarkably poor. RTs are highly variable with positively skewed frequency distributions, often modelled as an inverse Gaussian distribution reflecting a stochastic rise to threshold (diffusion process). However, latency distribution of saccades are very close to the reciprocal Normal, suggesting that ‘rate’ (reciprocal RT) may be the more fundamental variable. We explored whether this phenomenon extends to choice manual RTs. We recorded two-alternative choice RTs from 24 subjects, each with 4 blocks of 200 trials with two task difficulties (easy vs. difficult discrimination) and two instruction sets (urgent vs. accurate). We found that rate distributions were, indeed, very close to Normal, shifting to lower rates with increasing difficulty and accuracy, and for some blocks subjects they appeared to become left-truncated, but still close to Normal. Using autoregressive techniques, we found temporal sequential dependencies for lags of at least 3. We identified a transient and steady-state component in each block. Because rates were Normal, we were able to estimate autoregressive weights using the Box-Jenkins technique, and convert to a moving average model using z-transforms to show explicit dependence on stimulus input. We also found a spatial sequential dependence for the previous 3 lags depending on whether the laterality of previous trials was repeated or alternated. This was partially dissociated from temporal dependency as it only occurred in the easy tasks. We conclude that 2-alternative choice manual RT distributions are close to reciprocal Normal and not the inverse Gaussian. This is not consistent with stochastic rise to threshold models, and we propose a simple optimality model in which reward is maximized to yield to an optimal rate, and hence an optimal time to respond. We discuss how it might be implemented.

Durbin–Watson Test

Abstract: This text checks for independent errors when fitting a multiple regression model to time series data. Keywords: multiple regression; autocorrelation; test for independence

Methodology and Case Study of Sea Level Prediction Based on Secular Tide Gauge Data

Abstract: Based on the periodic, trending, and stochasticcharacteristics of secular tide gauge data, a predictive methodology using stochastic-dynamic model was present to the sea level change research. The periodic term was resolved by wavelet and spectrum analysis. Stepwise regression was applied to the trending term analysis. The residual sequence was fitted by autoregression moving average model. Least-squares iteration method was applied for parameter estimation ofthe superposition model, which was composed of significant period model, trending term model and the residual sequenceautoregression moving average model. The stochasticdynamic model is applied to 57 years' monthly mean sea level data from Tanggu tide gauge for case study. The results show that the predictive methodology based on stochastic-dynamic model is feasible and efficient in sea level change prediction. Considering the high accuracy of modeling and predicting, this methodology can be used as a reference for future studies in sea level change.

Joint seasonal ARMA approach for modeling of load forecast errors in planning studies

Abstract: To make informed and robust decisions in the probabilistic power system operation and planning process, it is critical to conduct multiple simulations of the generated combinations of wind and load parameters and their forecast errors to handle the variability and uncertainty of these time series. In order for the simulation results to be trustworthy, the simulated series must preserve the salient statistical characteristics of the real series. In this paper, we analyze day-ahead load forecast error data from multiple balancing authority locations and characterize statistical properties such as mean, standard deviation, autocorrelation, correlation between series, time-of-day bias, and time-of-day autocorrelation. We then construct and validate a seasonal autoregressive moving average (ARMA) model to model these characteristics, and use the model to jointly simulate day-ahead load forecast error series for all BAs.

Comparisons of Hyv\"arinen and pairwise estimators in two simple linear time series models

Abstract: The aim of this paper is to compare numerically the performance of two estimators based on Hyvarinen's local homogeneous scoring rule with that of the full and the pairwise maximum likelihood estimators. In particular, two different model settings, for which both full and pairwise maximum likelihood estimators can be obtained, have been considered: the first order autoregressive model (AR(1)) and the moving average model (MA(1)). Simulation studies highlight very different behaviours for the Hyvarinen scoring rule estimators relative to the pairwise likelihood estimators in these two settings.

First order threshold integer-valued moving average processes

Abstract: In this paper, we introduce a new threshold model with poisson innovation: Threshold Integer-Valued Moving Average model (TINMA). We derive the numerical char- acteristics of TINMA(1) model. Stationary and ergodicity are also obtained. The methods of estimation under analysis is Yule-Walker. Some simulation results illustrate the perfor- mance of the proposed method.

Integer-Valued Moving Average Models with Structural Changes

Abstract: It is frequent to encounter integer-valued time series which are small in value and show a trend having relatively large fluctuation. To handle such a matter, we present a new first order integer-valued moving average model process with structural changes. The models provide a flexible framework for modelling a wide range of dependence structures. Some statistical properties of the process are discussed and moment estimation is also given. Simulations are provided to give additional insight into the finite sample behaviour of the estimators.

A One Line Derivation of DCC: Application of a Vector Random Coefficient Moving Average Process

Abstract: One of the most widely-used multivariate conditional volatility models is the dynamic conditional correlation (or DCC) specification. However, the underlying stochastic process to derive DCC has not yet been established, which has made problematic the derivation of asymptotic properties of the Quasi-Maximum Likelihood Estimators. The paper shows that the DCC model can be obtained from a vector random coefficient moving average process, and derives the stationarity and invertibility conditions. The derivation of DCC from a vector random coefficient moving average process raises three important issues: (i) demonstrates that DCC is, in fact, a dynamic conditional covariance model of the returns shocks rather than a dynamic conditional correlation model; (ii) provides the motivation, which is presently missing, for standardization of the conditional covariance model to obtain the conditional correlation model; and (iii) shows that the appropriate ARCH or GARCH model for DCC is based on the standardized shocks rather than the returns shocks. The derivation of the regularity conditions should subsequently lead to a solid statistical foundation for the estimates of the DCC parameters.

Heteroskedasticity of Unknown Form in Spatial Autoregressive Models with Moving Average Disturbance Term

Abstract: In this study, I investigate the necessary condition for consistency of the maximum likelihood estimator (MLE) of spatial models with a spatial moving average process in the disturbance term. I show that the MLE of spatial autoregressive and spatial moving average parameters is generally inconsistent when heteroskedasticity is not considered in the estimation. I also show that the MLE of parameters of exogenous variables is inconsistent and determine its asymptotic bias. I provide simulation results to evaluate the performance of the MLE. The simulation results indicate that the MLE imposes a substantial amount of bias on both autoregressive and moving average parameters.

NARMAX model based pseudo-Hammerstein identification for rate-dependent hysteresis

Abstract: In this paper, a nonlinear auto-regressive moving average model with exogenous inputs(NARMAX) based pseudo-Hammerstein model is proposed for the identification of rate-dependent hysteresis. The presented model has the cascade structure comprised of a NARMAX model in series with an auto-regressive moving average(ARMA) model. In view of the multivalued mapping of hysteresis, a hysteretic operator is introduced to establish an expanded input space for the NARMAX model where the change tendency of the rate-dependent hysteresis can be extracted. To avoid the tedious dynamic back-propagation optimization for the auto-regressive(AR) parameters of the NARMAX model within the pseudo-Hammerstein model, a NARMAX model with the introduced hysteretic operator is applied to implement a preliminary identification for the rate-dependent hysteresis. Both the modified Akaike information criterion (MAIC) and the recursive least squaresfRLS) algorithm are employed to estimate an appropriate structure and the AR parameters of the NARMAX model. Subsequently, the Levenberg-Ma-rquardt(L-M) algorithm of the pseudo-Hammerstein model is developed to acquire an appropriate structure and the parameters of the ARMA model as well as the remaining parameters of the NARMAX model. Finally, numerical simulation results on a Duhem model of the piezoelectric actuators have demonstrated the effectiveness of the proposed model.

Symbolic ARMA Model Analysis

Abstract: ARMA models provide a parsimonious and flexible mechanism for modeling the evolution of a time series. Some useful measures of these models (e.g., the autocorrelation function or the spectral density function) are tedious to compute by hand. This paper uses a computer algebra system, not simulation, to calculate measures of interest associated with ARMA models.

Yule–Walker Equations

Abstract: In a stationary autoregressive time series of order p, the Yule–Walker equations are a set of p linear equations for the regression coefficients in terms of the autocorrelation functions. By estimating the latter, one can obtain estimates of the former. Keywords: stationary; autoregressive; autocorrelation

A New Method for 2-D Moving Average Model Parameter Estimation

Abstract: This paper presents a new method for the causal quarter-plane region of support two-dimensional (2-D) moving average (MA) model parameter estimation. The new approach is based on approximation of 2-D MA by the 2-D AR model. To achieve this aim, the corresponding relations are extended to a 2-D case and the related algorithm is presented. In this method, a 2-D series with the MA model has been approximated by a 2-D AR model with higher order and then the parameters of the AR model are estimated by the new method that is presented. Then the relation between the parameters of the 2-D AR and 2-D MA model is obtained and finally by using this relation, the parameters of the 2-D MA model are obtained. Since the proposed method does not involve complex and time consuming matrix computations, it is computationally efficient. The presented method also has good accuracy in standard deviation and mean value; a fact that has been shown by applying this method to a numerical example and presenting the results ...

Matrix time series analysis

Abstract: Many data sets in the sciences (broadly defined) deal with multiple sets of multivariate time series. The case of a single univariate time series is very well developed in the literature; and single multivariate series though less well studied have also been developed (under the rubric of vector time series). A class of matrix time series models is introduced for dealing with the situation where there are multiple sets of multivariate time series data. Explicit expressions for a matrix autoregressive model of order one and of order p along with its cross-autocorrelation functions are derived. This includes obtaining the infinite order moving average analogues of these matrix time series. Stationarity conditions are also provided. Parameters of the proposed matrix time series model are estimated by ordinary and generalized least squares method, and maximum likelihood estimation method.

Time-Varying Moving Average Model for Autocovariance Nonstationary Time Series

Abstract: In time series analysis, fitting the Moving Average (MA) model is more complicated than Autoregressive (AR) models because the error terms are not observable. This means that iterative nonlinear fitting procedures need to be used in place of linear least squares. In this paper, Time-Varying Moving Average (TVMA) models are proposed for an autocovariance nonstationary time series. Through statistical analysis, the parameter estimates of the MA models demonstrate high statistical efficiency. The Akaike Information Criterion (AIC) analyses and the simulations by the TVMA models were carried out. The suggestion about the TVMA model selection is given at the end. This research is useful for analyzing an autocovariance nonstationary time series in theoretical and practical fields.

On the log quantile difference of the temporal aggregation of a stable moving average process

Abstract: A formula is derived for the log quantile difference of the temporal aggregation of some types of stable moving average processes, MA(q). The shape of the log quantile difference as a function of the aggregation level is examined and shown to be dependent on the parameters of the moving average process but not the quantile levels. The classes of invertible, stable MA(1) and MA(2) processes are examined in more detail.

Estimation Bias and Feasible Conditional Forecasts from the First-Order Moving Average Model

Abstract: The quasi-maximum likelihood estimator (QMLE) of parameters in the first-order moving average model can be biased in finite samples. We develop the second-order analytical bias of the QMLE and investigate whether this estimation bias can lead to biased feasible optimal forecasts conditional on the available sample observations. We find that the feasible multiple-step-ahead forecasts are unbiased under any nonnormal distribution, and the one-step-ahead forecast is unbiased under symmetric distributions.