Abstract: This is a "spatial autocorrelation analysis" of spatial autocorrelation. I use the 1-dimension spatial autocorrelation function (ACF) and partial autocorrelation function (PACF) to analyze four kinds of weight function in common use for the 2-dimensional spatial autocorrelation model. The aim of this study is at how to select a proper weight function to construct a spatial contiguity matrix for spatial analysis. The scopes of application of different weight functions are defined in terms of the characters of their ACFs and PACFs.

Abstract: This simulation study examined the performance of the curve-of-factors model (COFM) when autocorrelation and growth processes were present in the first-level factor structure. In addition to the standard curve-of factors growth model, 2 new models were examined: one COFM that included a first-order autoregressive autocorrelation parameter, and a second model that included first-order autoregressive and moving average autocorrelation parameters. The results indicated that the estimates of the overall trend in the data were accurate regardless of model specification across most conditions. Variance components estimates were biased across many conditions but improved as sample size and series length increased. In general, the two models that incorporated autocorrelation parameters performed well when sample size and series length were large. The COFM had the best overall performance.

Abstract: Most of physical experiments are usually described as repeated measurements of some random variables. Experimental data registered by on‐line computers form time series of outcomes. The frequencies of different outcomes are compared with the probabilities provided by the algorithms of quantum theory (QT). In spite of statistical predictions of QT a claim was made that it provided the most complete description of the data and of the underlying physical phenomena. This claim could be easily rejected if some fine structures, averaged out in the standard descriptive statistical analysis, were found in time series of experimental data. To search for these structures one has to use more subtle statistical tools which were developed to study time series produced by various stochastic processes. In this talk we review some of these tools. As an example we show how the standard descriptive statistical analysis of the data is unable to reveal a fine structure in a simulated sample of AR (2) stochastic process. We emphasize once again that the violation of Bell inequalities gives no information on the completeness or the non locality of QT. The appropriate way to test the completeness of quantum theory is to search for fine structures in time series of the experimental data by means of the purity tests or by studying the autocorrelation and partial autocorrelation functions.

Abstract: The periodic autoregressive model, a particular structure of the Box & Jenkins family, denoted by PAR (p), is employed to model the series of hydrological streamflow used for estimating the operational costs of the Brazilian hydro-thermal optimal dispatch. Recently, some aspects of this approachbegan to be studied and several researches on this topic are being developed. This paper focuses on the identification stage of the orders p of these models. Nowadays, the identification is based on evaluating the significance of the coefficients of the partial autocorrelation function (PACF), based on the asymptoticresults of Quenouille. The purpose of this study is on the application of the computer-intensive Bootstraptechnique to estimate the significance of such coefficients. The results show that identification via Bootstrap is considerably more parsimonious, leading to the identification of lower orders in most cases andcorroborating some points raised in previous studies on the traditional approach.

Abstract: In two recent decades, the resultant changes in global climate were one of the main issues propounded among water resources' experts in the country; and temperature and humidity forecasts can efficiently be applied in decision making and optimum usage of water resources. Temperature and humidity have irrefutable effects on hydrologic cycle, production cycle of agricultural products, water consumptions (specifically agriculture), human efforts and environment. Utilization of Statistical distribution is one of the main rules that have the capability of forecasting hydrologic events with largeness and distinctive incidence probability. Theory of time series is implemented by two main aims of perception or modeling random mechanisms and prospect of future amounts of series based on its past. Relative humidity and the average monthly temperature of Ahvaz synoptic station is used in present research of 20-year-old statistic. And a proper model is achieved by applying time series analysis software (ITSM) in accordance with ARIMA model and autocorrelation and partial autocorrelation method and by evaluation of all probabilistic models in terms of being static and study of parameters and types of models, in order to forecast average monthly temperature ARIMA (0,0,1)×(0,1,1) 12 and forecast monthly relative humidity ARIMA (0,0,1)×(2,1,2) 12 based on Box-Jenkins algorithm and after validation and evaluation of model, we determined that selection of given models was very proper and forecast of relative humidity measure and average monthly temperature is implemented in agricultural years of 2009-2010 and 2010-2011 by them.

Abstract: Nous expliquons le lien entre fonction d'autocorrélation pour processus stationnaire en temps continu et fonction caractéristique réelle, et passons en revue les conditions suffisantes pour qu'une fonction donnée soit une telle fonction d'autocorrélation. Nous fournissons également des constructions probabilistes pour la reformulation, dans ce contexte, des théorèmes de Pólya (1949) sur les fonctions caractéristiques et de Young (1913) sur l'analyse de Fourier. Nos constructions couvrent le cas de processus à loi marginale infiniment divisible et de variance finie.

Abstract: This paper presents a way to use the recurrent quadratic Volterra system to forecast the wind power output. The recurrent quadratic Volterra system is a second-order polynomial equation that uses the output data as feedback recursively. The Volterra system is extracted from the weights of the Recurrent Neural Network. During this process, three innovative techniques are used. In order to make Volterra kernels from the combination of weights, the activation function is approximated to the high-order polynomial function by using the Lagrangian interpolation. Furthermore, the memory of the Volterra system is also identified using the Partial Autocorrelation Function. After building the Volterra system, the 15 and 30-minutes ahead of wind power output is forecasted with confidence intervals at the 95% confidence level. The confidence interval is calculated using the multi-linear regression techniques. The stability of the recurrent Volterra system is also considered by the heuristic method.

Abstract: This paper presents a new method of detecting multi-periodicities in a seasonal time series. Conventional methods such as the average power spectrum or the autocorrelation function plot have been used in detecting multiple periodicities. However, there are numerous cases where those methods either fail, or lead to incorrectly detected periods. This, in turn in applications, produces improper models and results in larger forecasting errors. There is a strong need for a new approach to detecting multi-periodicities. This paper tends to fill this gap by proposing a new method which relies on a mathematical instrument, called the Average Power Function of Noise (APFN) of a time series. APFN has a prominent property that it has a strict local minimum at each period of the time series. This characteristic helps one in detecting periods in time series. Unlike the power spectrum method where it is assumed that the time series is composed of sinusoidal functions of different frequencies, in APFN it is assumed that the time series is periodic, the unique and a much weaker assumption. Therefore, this new instrument is expected to be more powerful in multi-periodicity detection than both the autocorrelation function plot and the average power spectrum. Properties of APFN and applications of the new method in periodicity detection and in forecasting are presented.

Abstract: Ramanagaram and Siddlaghatta were class I reeling cocoon markets in Karnataka. The present study was to determine the market integration between Ramanagaram and Siddlaghatta markets and to forecast the price and arrival of cocoon. The study was exclusively based on secondary data and the study period was ten years from 1998-99 to 2007- 08. Correlation technique and concurrent deviation method was used to determine the market integration. Auto Regressive Integrated Moving Average (ARIMA) model was used to forecast the arrival and price. Suitable model was identified based on the Autocorrelation function and Partial Autocorrelation Function. The adequacy of the model was judged based on the values of Box-Pierce Q statistics and Akike Information Co-efficient (AIC). Market integration is found to be perfect between two markets. Forecasted values of arrival showed increasing trend in both the markets and price showed decreasing trend in Siddlaghatta market.

Abstract: In this paper, we extend the works by [1-5] accounting for autocorrelation both in the time specific effect as well as the remainder error term. Several transformations are proposed to circumvent the double autocorrelation problem in some specific cases. Estimation procedures are then derived.

Abstract: In this paper, we propose a novel hybrid multi-model approach for rainfall forecasting. In this multi-model system we have incorporated an efficient input selection technique, a set of distinct predictive models with carefully selected parameter settings, a variable selection method to rank (weight) the models before combining their outputs and a simple weighted average to combine the forecasts of all the models. The input selection technique is based on auto correlation and partial autocorrelation function, the predictive models are stepwise linear regression, partial least square regression, multivariate adaptive regression spline, radial basis kernel gaussian process and multi layer perceptron with quasi Newton optimization. The model ranking technique is based multi response sparse regression, which rank the variables (here models) according to their predictive performance (here forecasting). We have utilized this rank to use it as the wegiht in the weighted average of the forecast combination of the models. We have applied this novel multi model approach in forecasting daily rainfall of rainy season of Fukuoka city of Japan. We have used several performance metrics to quantify the predictive quality of the hybrid model. The results suggest that the novel hybrid multi-model approach can make efficient and persistent short term rainfall forecast.

Abstract: OF THE DISSERTATION ON ORDER IDENTIFICATION OF TIME SERIES MODELS AND ITS APPLICATIONS by Shuhao Chen Dissertation Director: Rong Chen My thesis focuses on the order identification schemes of the widely-used time series model Autoregressive Integrated Moving-Average (ARIMA) model and the applications of the order determination methods. The first part investigates the impact of dependent but uncorrelated innovations (errors) on the traditional autoregressive integrated moving average (ARIMA) model order determination schemes such as autocorrelation function (ACF), partial autocorrelation function (PACF), extended autocorrelation function (EACF) and unit-root test. We also propose a new order determination scheme to address those impacts and can be used to time series sequences with uncorrelated innovations. In the second part, a unified approach for the tentative specification of both the seasonal and nonseasonal orders of general multiplicative seasonal model is proposed. This new approach has the advantages of determining the seasonal and nonseasonal orders simultaneously and automatically.

Abstract: Box-Jenkins method of time series in modeling the signal of quartz flex accelerometer is studied in the paper. Firstly, a JSD-I/A quartz flex accelerometer is placed on a level test bench, and the output signal of the JSD-I/A quartz flex accelerometer is acquired. Secondly, the acquired signal of the JSD-I/A quartz flex accelerometer is preprocessed by Db3 wavelet denoising, trend items exacting, and standardized processing. Thirdly, The statistical characteristics of autocorrelation function (ACF) and partial autocorrelation function (PACF) of the processed time series data are analyzed, and the results show that ACF presents tailing characteristic and PACF presents censoring characteristic after 12th order. So AR(12) model is suitable for modeling the processed data of the JSD-I/A quartz flex accelerometer. Fourthly, the AR(12) model’s parameters are estimated by four methods, named least square method (LSM), Yule-Walker method, LUD method and Burg method, respectively. The fitting effects by residuals sum of squares (RSS) of the above estimation methods are compared and the results show that LSM outperforms the other three estimation methods.

Abstract: Ground movement data of a monitoring point from 2001 to 2010 in a mining area were analyzed by statistical methods.The results show that the autocorrelation function(AC) and partial autocorrelation function(PAC) of the sample data are clearly tail-dragged,which meet with ARMA(p,q) model.On this basis,parameters estimation and checking of model was done by the software EViews,ARMA prediction model of ground surface movement was established.Through comparing the forecasting results from the model with the monitoring data,it shows that the prediction model is a useful method with good precision,especially under short time step prediction.

Abstract: In this paper, the authors identified a detailed time-series model according to the transport volume impact factor combined with the autocorrelation factor (ACF) and the partial autocorrelation factor (PACF) Legend. They estimated the parameter and diagnosed the model through logistic regression and ARIMA technology. The results showed that model 1 is not sensitive to external factors while model 2 is; model 2 is thus the best one.

Abstract: PROBLEM TO BE SOLVED: To provide a device and method for extraction of a vocal tract cross section function, capable of excellently controlling voice quality even for a voice signal of a high sampling frequency. SOLUTION: The extraction device of the vocal tract cross section function extracts the vocal tract cross section function from a digitalized voice signal. The device includes: a frame segmenting unit 10 for segmenting the digitalized voice signal into frame units; a band divider 20 for dividing each voice signal into a low frequency component and a high frequency component; a flattening processing unit 30 for flattening a frequency characteristic of each component; an autocorrelation function conversion unit 40 for converting each component into an autocorrelation function; an LSP (Line Spectrum Pair) parameter extraction unit 50 for extracting the LSP parameter from the autocorrelation function of each component; an LSP parameter connection 60 for connecting the LSP parameter of each component; a PARCOR (Partial Autocorrelation Coefficients)coefficient conversion unit 70 for converting the connected LSP parameter into a PARCOR coefficient; and vocal tract cross section function conversion unit 80 for converting the PARCOR coefficient into the vocal cross section function. COPYRIGHT: (C)2011,JPO&INPIT

Abstract: The effect of data pre-processing while developing artificial intelligence (AI) -based data-driven techniques, such as artificial neural networks (ANN), model trees (MT) and linear genetic programming (LGP), is studied for Pawana Reservoir in Maharashtra, India. The daily one-step-ahead inflow forecasts are compared with flows generated from a univariate autoregressive integrated moving average (ARIMA) model. For the full-year data series, a large error is found mainly due to the occurrence of zero values, since the reservoir is located in an intermittent river. Hence, all the techniques are evaluated using two data series: 18 years of daily full-year inflow data (from 1 January to 31 December); and 18 years of daily monsoon season inflow data (from 1 June to 31 October) to take into account the intermittent nature of the data. The relevant range of inputs for each category is selected based on autocorrelation and partial autocorrelation analyses of the inflow series. Conventional pre-processing ...

Abstract: Problem statement: Most of Seasonal Autoregressive Integrated Moving Average (SARIMA) models that used for forecasting seasonal time series are multiplicative SARIMA models. These models assume that there is a significant parameter as a result of multiplication between nonseasonal and seasonal parameters without testing by certain statistical test. Moreover, most popular statistical software such as MINITAB and SPSS only has facility to fit a multiplicative model. The aim of this research is to propose a new procedure for indentifying the most appropriate order of SARIMA model whether it involves subset, multiplicative or additive order. In particular, the study examined whether a multiplicative parameter existed in the SARIMA model. Approach: Theoretical derivation about Autocorrelation (ACF) and Partial Autocorrelation (PACF) functions from subset, multiplicative and additive SARIMA model was firstly discussed and then R program was used to create the graphics of these theoretical ACF and PACF. Then, two monthly datasets were used as case studies, i.e. the international airline passenger data and series about the number of tourist arrivals to Bali, Indonesia. The model identification step to determine the order of ARIMA model was done by using MINITAB program and the model estimation step used SAS program to test whether the model consisted of subset, multiplicative or additive order. Results: The theoretical ACF and PACF showed that subset, multiplicative and additive SARIMA models have different patterns, especially at the lag as a result of multiplication between non-seasonal and seasonal lags. Modeling of the airline data yielded a subset SARIMA model as the best model, whereas an additive SARIMA model is the best model for forecasting the number of tourist arrivals to Bali. Conclusion: Both of case studies showed that a multiplicative SARIMA model was not the best model for forecasting these data. The comparison evaluation showed that subset and additive SARIMA models gave more accurate forecasted values at out-sample datasets than multiplicative SARIMA model for airline and tourist arrivals datasets respectively. This study is valuable contribution to the Box-Jenkins procedure particularly at the model identification and estimation steps in SARIMA model. Further work involving multiple seasonal ARIMA models, such as short term load data forecasting in certain countries, may provide further insights regarding the subset, multiplicative or additive orders.