The autoregressive-integrated moving average (AMIRA) process plays an essential role in time series models. Classical method of finding the maximum likelihood (ML) estimate of the parameters in an ARIMA(p; d; q) model consists of evaluating the likelihood function through the Box-Jenkins approach or the Innovations Algorithm and optimizing it by numerical methods such as the quasi-Newton algorithms. However, these approaches have several drawbacks. The quasi-Newton methods tend to be unstable when the likelihood function is highly nonlinear. In this paper, we consider a state space representation of the ARIMA(p; d; q) process. The likelihood function can be easily expressed by the Kalman filter and the ML estimates can be obtained through a combination of Kalman smoother and the EM Algorithm. The updating equations in the EM algorithm possess a simple analytical form. A quasi-Newton scheme has also been implemented to accelerate the convergence of the EM Algorithm. The simulations studies show that the EM algorithm is more robust to starting values and the number of parameters, and the quasi-Newton acceleration scheme significantly improves the convergence rate of the EM algorithm. / 差分自回歸移動平均(AMIRA)模型在時間序列模型中有著重要地位。ARIMA模型的傳統極大似然估計方法通過Box-Jenkins方法或者新息算法(Innovations Algorithm)計算出似然函數，再通過擬牛頓(quasi-Newton)法等數值方法將之極大化，從而得到參數的極大似然估計。然而，此類方法在一定條件下存在缺陷。例如，當似然函數高度非線性時，擬牛頓法表現出不穩定的現象。本文考慮ARIMA模型的一種狀態空間(state-space)模型表示。在此表示下，參數的似然函數可以通過卡爾曼濾波算法計算，而參數的極大似然估計可以通過卡爾曼平滑和EM算法簡單得出。本問題中EM算法的迭代公式有簡潔的解析形式。同時，我們進一步考慮了一個擬牛頓加速算法來加快EM算法的收斂速度。通過模擬實驗我們發現，對於不同的初始值和參數個數，EM算法比擬牛頓法更為穩健。同時，擬牛頓的加速算法可以顯著加快EM算法的收斂速度。 / Huang, Rui. / Thesis M.Phil. Chinese University of Hong Kong 2015. / Includes bibliographical references (leaves 57-58). / Abstracts also in Chinese. / Title from PDF title page (viewed on 06, October, 2016). / Detailed summary in vernacular field only.

Thesis (Ph. D.)--University of Chicago, Graduate School of Business, December 2000. / Includes bibliographical references. Also available on the Internet.

Thesis (M.Statistics) North-West University, Mafikeng Campus, 2010

by Lawrence Chi-Ho Lee. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1998. / Includes bibliographical references (leaves 91-97). / Abstract also in Chinese. / Chapter Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- The Importance of Forecasting --- p.1 / Chapter 1.2 --- Objective --- p.3 / Chapter Chapter 2 --- Holt-Winters Forecasting Procedure --- p.6 / Chapter 2.1 --- Exponential Smoothing and Holt-Winters Method --- p.6 / Chapter 2.2 --- Relationships Between Holt-Winters models and ARIMA Models --- p.13 / Chapter 2.2.1 --- A Steady Model --- p.14 / Chapter 2.2.2 --- A Growth Model --- p.15 / Chapter 2.2.3 --- The Three-Parameter Holt-Winters Model --- p.18 / Chapter 2.3 --- Some Practical Issues --- p.19 / Chapter 2.3.1 --- Normalizing the Seasonal Factors --- p.20 / Chapter 2.3.2 --- Choosing Starting Values --- p.20 / Chapter 2.3.3 --- Choosing the Smoothing Parameters --- p.22 / Chapter Chapter 3 --- Methods of Constructing Simultaneous Prediction Intervals --- p.24 / Chapter 3.1 --- Three Approximation Procedures --- p.25 / Chapter 3.1.1 --- Bonferroni-type Inequality --- p.26 / Chapter 3.1.2 --- Product-type Inequality --- p.28 / Chapter 3.1.3 --- Chi-square-type Inequality --- p.30 / Chapter 3.2 --- The 'Exact' Procedure --- p.31 / Chapter 3.3 --- Summary --- p.32 / Chapter Chapter 4 --- An Illustrative Example --- p.33 / Table 4.1 - 4.7 --- p.47 / Figure 4.1 - 4.5 --- p.55 / Chapter Chapter 5 --- Simulation Study --- p.60 / Chapter 5.1 --- Holt-Winters Forecasting Procedure for Optimal Model --- p.60 / Chapter 5.2 --- Holt-Winters Forecasting Procedure for Some Non-optimal Models --- p.66 / Chapter 5.3 --- A Comparison of Box-Jenkins Method and Holt-Winters Forecasting Procedure --- p.68 / Chapter 5.4 --- Conclusion --- p.74 / Table 5.1-5.10 --- p.75 / Chapter Chapter 6 --- Further Research --- p.82 / APPENDIXES --- p.87 / REFERENCES --- p.91

Thesis (M.S.)--West Virginia University, 2008. / Title from document title page. Document formatted into pages; contains x, 111 p. : ill. Includes abstract. Includes bibliographical references (p. 102-106).

A computer model simulating the electrical activity of muscles of the upper arm during elbow motion is presented. The output of the model is an Electromyographic (EMG) signal. System identification is performed on the EMG signals using autoregressive moving average (ARMA) modelling. The calculated ARMA coefficients are then used as the feature set for pattern recognition. Pattern recognition is performed on the EMG signals to attempt to identify which of four possible motions is producing the signal. The results of pattern recognition are compared with results from pattern recognition of real EMG signals. The model is shown to be useful in predicting general trends found in the real data, but is not robust enough to predict accurate quantitative results. Simplifying assumptions about the filtering effects of body tissue, and about the size and position of muscles, are conjectured to be the most likely reasons the model is not quantitatively accurate. / Graduation date: 1992

University of Macau / Faculty of Science and Technology / Department of Mathematics

The concise description of one- and multidimensional stationary and non stationary vehicle loading histories for fatigue analysis using stochastic process theory is presented in this study. The load history is considered to have stationary random and nonstationary mean and variance content. The stationary variations are represented by a class of time series referred to as Autoregressive Moving Average (ARMA) models, while a Fourier series is used to account for the variation of the mean and variance. Due to the use of random phase angles in the Fourier series, an ensemble of mean and variance variations is obtained. The methods of nonparametric statistics are used to determine the success of the modeling of nonstationarity. Justification of the method is obtained through comparison of rainflow cycle distributions and resulting fatigue lives of original and simulated loadings. Due to the relatively small number of Fourier coefficients needed together with the use of ARMA models, a concise description of complex loadings is achieved. The overall frequency content and sequential information of the load history is statistically preserved. An ensemble of load histories can be constructed on-line with minimal computer storage capacity as used in testing equipment. The method can be used in a diversity of fields where a concise representation of random loadings is desired. / Ph. D.

by Moon-Tong Chan. / Thesis submitted in: December 1997. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1998. / Includes bibliographical references (leaves 123-124). / Abstract also in Chinese. / Chapter Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- The Data Set --- p.8 / Chapter Chapter 2 --- The Box-Jenkins Time Series Models --- p.15 / Chapter 2.1 --- The White-noise Process --- p.16 / Chapter 2.2 --- Stationarity of Time Series --- p.17 / Chapter 2.3 --- Differencing --- p.19 / Chapter 2.4 --- Seasonal ARIMA Models - SARIMA Models --- p.20 / Chapter 2.5 --- Intervention Models --- p.22 / Chapter 2.6 --- The Three Phases of ARMA Procedure --- p.24 / Chapter Chapter 3 --- Seasonal ARMA Models with Several Mean Levels --- p.38 / Chapter 3.1 --- Review of Linear Models --- p.40 / Chapter 3.1.1 --- Method of Weighted Least Squares --- p.41 / Chapter 3.2 --- The Proposed Model --- p.41 / Chapter 3.2.1 --- The Weightings --- p.43 / Chapter 3.2.2 --- Selection of Submodels --- p.45 / Chapter 3.2.3 --- Estimation of Model (3.4) --- p.46 / Chapter 3.3 --- Model Adequacy Checking --- p.55 / Chapter 3.3.1 --- Checking of Independence of Residuals --- p.56 / Chapter 3.3.2 --- Checking of Normality of Residuals --- p.58 / Chapter 3.4 --- Forecasting --- p.62 / Chapter Chapter 4 --- Comparison --- p.77 / Chapter 4.1 --- Similarities and Differences Between the Two Models --- p.78 / Chapter 4.2 --- Model Comparative Criterion --- p.81 / Chapter 4.2.1 --- Model Fitting Comparison --- p.82 / Chapter 4.2.2 --- Model Forecasting Comparison --- p.83 / Chapter 4.3 --- Conclusion --- p.90 / Chapter 4.4 --- Generation of Predicted Hourly Calls --- p.91 / Chapter 4.5 --- Extension --- p.92 / Appendix A --- p.97 / Appendix B --- p.105 / Appendix C --- p.122 / References --- p.123

Solar radiation is a primary driving force behind a number of solar energy applications such as photovoltaic systems for electricity generation amongst others. Hence, the accurate modelling and prediction of the solar flux incident at a particular location, is essential for the design and performance prediction of solar energy conversion systems. In this regard, literature shows that time series models such as the Box-Jenkins Seasonal/Non-seasonal Autoregressive Integrated Moving Average (S/ARIMA) stochastic models have considerable efficacy to describe, monitor and forecast solar radiation data series at various sites on the earths surface (see e.g. Reikard, 2009). This success is attributable to their ability to capture the stochastic component of the irradiance series due to the effects of the ever-changing atmospheric conditions. On the other hand at the top of the atmosphere, there are no such conditions and deterministic models which have been used successfully to model extra-terrestrial solar radiation. One such modelling procedure is the use of a sinusoidal predictor at determined harmonic (Fourier) frequencies to capture the inherent periodicities (seasonalities) due to the diurnal cycle. We combine this deterministic model component and SARIMA models to construct harmonically coupled SARIMA (HCSARIMA) models to model the resulting mixture of stochastic and deterministic components of solar radiation recorded at the earths surface. A comparative study of these two classes of models is undertaken for the horizontal global solar irradiance incident on the solar panels at UKZN Howard College (UKZN HC), located at 29.9º South, 30.98º East with elevation, 151.3m. The results indicated that both SARIMA and HCSARIMA models are good in describing the underlying data generating processes for all data series with respect to different diagnostics. In terms of the predictive ability, the HCSARIMA models generally had a competitive edge over the SARIMA models in most cases. Also, a tentative study of long range dependence (long memory) shows this phenomenon to be inherent in high frequency data series. Therefore autoregressive fractionally integrated moving average (ARFIMA) models are recommended for further studies on high frequency irradiance. / M.Sc. University of KwaZulu-Natal, Durban 2014.