Noise Modeling

2017 ◽  
Author(s):  
Richard McCleary ◽  
David McDowall ◽  
Bradley J. Bartos
Keyword(s):  
Time Series ◽  
White Noise ◽  
Autocorrelation Function ◽  
Model Building ◽  
Moving Average ◽  
Information Criteria ◽  
Noise Model ◽  
Adequate Model ◽  
Noise Modeling ◽  
Modeling Strategy

Chapter 3 introduces the Box-Jenkins AutoRegressive Integrated Moving Average (ARIMA) noise modeling strategy. The strategy begins with a test of the Normality assumption using a Kolomogov-Smirnov (KS) statistic. Non-Normal time series are transformed with a Box-Cox procedure is applied. A tentative ARIMA noise model is then identified from a sample AutoCorrelation function (ACF). If the sample ACF identifies a nonstationary model, the time series is differenced. Integer orders p and q of the underlying autoregressive and moving average structures are then identified from the ACF and partial autocorrelation function (PACF). Parameters of the tentative ARIMA noise model are estimated with maximum likelihood methods. If the estimates lie within the stationary-invertible bounds and are statistically significant, the residuals of the tentative model are diagnosed to determine whether the model’s residuals are not different than white noise. If the tentative model’s residuals satisfy this assumption, the statistically adequate model is accepted. Otherwise, the identification-estimation-diagnosis ARIMA noise model-building strategy continues iteratively until it yields a statistically adequate model. The Box-Jenkins ARIMA noise modeling strategy is illustrated with detailed analyses of twelve time series. The example analyses include non-Normal time series, stationary white noise, autoregressive and moving average time series, nonstationary time series, and seasonal time series. The time series models built in Chapter 3 are re-introduced in later chapters. Chapter 3 concludes with a discussion and demonstration of auxiliary modeling procedures that are not part of the Box-Jenkins strategy. These auxiliary procedures include the use of information criteria to compare models, unit root tests of stationarity, and co-integration.

Intervention Modeling

2017 ◽  
Author(s):  
Richard McCleary ◽  
David McDowall ◽  
Bradley J. Bartos
Keyword(s):  
Time Series ◽  
Autocorrelation Function ◽  
Moving Average ◽  
Intervention Model ◽  
Noise Component ◽  
Autoregressive Integrated Moving Average ◽  
Noise Function ◽  
Modeling Strategy ◽  
The Impact ◽  
True Structure

The general AutoRegressive Integrated Moving Average (ARIMA) model can be written as the sum of noise and exogenous components. If an exogenous impact is trivially small, the noise component can be identified with the conventional modeling strategy. If the impact is nontrivial or unknown, the sample AutoCorrelation Function (ACF) will be distorted in unknown ways. Although this problem can be solved most simply when the outcome of interest time series is long and well-behaved, these time series are unfortunately uncommon. The preferred alternative requires that the structure of the intervention is known, allowing the noise function to be identified from the residualized time series. Although few substantive theories specify the “true” structure of the intervention, most specify the dichotomous onset and duration of an impact. Chapter 5 describes this strategy for building an ARIMA intervention model and demonstrates its application to example interventions with abrupt and permanent, gradually accruing, gradually decaying, and complex impacts.

The Noise Component:N(at)

2019 ◽  
pp. 48-97
Author(s):  
David McDowall ◽  
Richard McCleary ◽  
Bradley J. Bartos
Keyword(s):  
Time Series ◽  
White Noise ◽  
Moving Average ◽  
Nonstationary Time Series ◽  
Time Series Models ◽  
Seasonal Time Series ◽  
Experience Of Time ◽  
Collective Experience ◽  
Modeling Strategy ◽  
Noise Models

Chapter 3 develops the methods or strategies for building ARIMA noise models. At one level, the iterative identify-estimate-diagnose modeling strategy proposed by Box and Jenkins has changed little. At another level, the collective experience of time series experimenters leads to several modifications of the strategy. For the most part, these changes are aimed at solving practical problems. Compared to the 1970s, for example, modelers today pay more attention to transformations and to the usefulness and interpretability of an ARIMA model. The Box-Jenkins ARIMA noise modeling strategy is illustrated with detailed analyses of twelve time series. The example analyses include non-Normal time series, stationary white noise, autoregressive and moving average time series, nonstationary time series, and seasonal time series. The time series models build in Chapter 3 are re-introduced in later chapters.

Predicting Daily Confirmed COVID-19 Cases in India

2021 ◽  
pp. 34-51
Author(s):  
Sudip Singh
Keyword(s):  
Time Series ◽  
Root Mean Square Error ◽  
Autocorrelation Function ◽  
Moving Average ◽  
Arima Model ◽  
Family Welfare ◽  
Mean Square ◽  
Univariate Time Series ◽  
Partial Autocorrelation Function ◽  
Auto Regressive

India, with a population of over 1.38 billion, is facing high number of daily COVID-19 confirmed cases. In this chapter, the authors have applied ARIMA model (auto-regressive integrated moving average) to predict daily confirmed COVID-19 cases in India. Detailed univariate time series analysis was conducted on daily confirmed data from 19.03.2020 to 28.07.2020, and the predictions from the model were satisfactory with root mean square error (RSME) of 7,103. Data for this study was obtained from various reliable sources, including the Ministry of Health and Family Welfare (MoHFW) and http://covid19india.org/. The model identified was ARIMA(1,1,1) based on time series decomposition, autocorrelation function (ACF), and partial autocorrelation function (PACF).

Auxiliary Modeling Procedures

2019 ◽  
pp. 136-153
Author(s):  
David McDowall ◽  
Richard McCleary ◽  
Bradley J. Bartos
Keyword(s):  
Time Series ◽  
Error Correction ◽  
Unit Root ◽  
Model Building ◽  
Causal Effect ◽  
Information Criteria ◽  
Unit Root Tests ◽  
Error Correction Models ◽  
Control Time ◽  
Model Building Strategy

Chapter 5 describes three sets of auxiliary methods that have emerged as add-on supplements to the traditional ARIMA model-building strategy. First, Bayesian information criteria (BIC) can be used to inform incremental modeling decisions. BICs are also the basis for the Bayesian hypothesis tests introduced in Chapter 6. Second, unit root tests can be used to inform differencing decisions. Used appropriately, unit root tests guard against over-differencing. Finally, co-integration and error correction models have become a popular way of representing the behavior of two time series that follow a shared path. We use the principle of co-integration to define the ideal control time series. Put simply, a time series and its ideal counterfactual control time series are co-integrated up the time of the intervention. At that point, if the two time series diverge, the magnitude of their divergence is taken as the causal effect of the intervention.

scholarly journals Forecasting Rice Productivity and Production of Odisha, India, Using Autoregressive Integrated Moving Average Models

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Rahul Tripathi ◽  
A. K. Nayak ◽  
R. Raja ◽  
Mohammad Shahid ◽  
Anjani Kumar ◽  
...  
Keyword(s):  
Autocorrelation Function ◽  
Moving Average ◽  
Selection Criterion ◽  
Information Criteria ◽  
Arima Models ◽  
Autoregressive Integrated Moving Average ◽  
Rice Productivity ◽  
Rice Area ◽  
Moving Average Models ◽  
Partial Autocorrelation Function

Forecasting of rice area, production, and productivity of Odisha was made from the historical data of 1950-51 to 2008-09 by using univariate autoregressive integrated moving average (ARIMA) models and was compared with the forecasted all Indian data. The autoregressive (p) and moving average (q) parameters were identified based on the significant spikes in the plots of partial autocorrelation function (PACF) and autocorrelation function (ACF) of the different time series. ARIMA (2, 1, 0) model was found suitable for all Indian rice productivity and production, whereas ARIMA (1, 1, 1) was best fitted for forecasting of rice productivity and production in Odisha. Prediction was made for the immediate next three years, that is, 2007-08, 2008-09, and 2009-10, using the best fitted ARIMA models based on minimum value of the selection criterion, that is, Akaike information criteria (AIC) and Schwarz-Bayesian information criteria (SBC). The performances of models were validated by comparing with percentage deviation from the actual values and mean absolute percent error (MAPE), which was found to be 0.61 and 2.99% for the area under rice in Odisha and India, respectively. Similarly for prediction of rice production and productivity in Odisha and India, the MAPE was found to be less than 6%.

Forecasting of milk production in India with ARIMA and VAR time series models

2016 ◽  
Vol 35 (1) ◽  
Author(s):  
Sagar Surendra Deshmukh ◽  
R. Paramasivam
Keyword(s):  
Milk Production ◽  
Autocorrelation Function ◽  
Moving Average ◽  
Dairy Industry ◽  
Secondary Data ◽  
Information Criteria ◽  
Policy Implications ◽  
Test Reliability ◽  
Percentage Error ◽  
Future Production

India is witnessing tremendous growth in dairy industry. The milk production has increased from 20 million tonnes in 1961 to 132 million tonnes in 2012-13. India has been retaining its number one position in milk production for many years. Dairy Industry in India is growing at the rate of 10% per annum. Considering this, it is essential to know the future production to improve and sustain the growth and development of sector. The objective of the study is to find out most suitable forecasting method for milk production for sustainable future production and policy implications. The data used in study is secondary data, collected from FAOSTAT (1961 to 2012) and NDDB (1991 to 2012). Stationarity of data was checked with Autocorrelation Function (ACF) and Partial autocorrelation function (PACF), after confirming the stationarity, Autoregressive Integrated Moving Average (ARIMA) and Vector Autoregression (VAR) models were used. Akaike Information Criteria (AIC), Schwartz Bayesian Criteria (SBC), Mean Absolute Percentage Error (MAPE), R square and RMSE were used to test reliability of model. The results indicate that ARIMA (1, 1, 1) is more suitable method with the use of SPSS software package for forecasting of milk. Milk production is expected to be 160 million tonnes by 2017.

scholarly journals ANALISIS TIME SERIES DENGAN METODE ARIMA DAN APLIKASINYA

2020 ◽  
Vol 1 (2) ◽  
pp. 26-36
Author(s):  
Fathorrozi Ariyanto ◽  
Moh. Badri Tamam
Keyword(s):  
Time Series ◽  
Autocorrelation Function ◽  
Moving Average ◽  
Autoregressive Integrated Moving Average ◽  
Partial Autocorrelation Function ◽  
Model Time Series

Model time series yang sangat terkenal adalah model Autoregressive Integrated Moving Average (ARIMA) yang dikembangkan oleh George E. P. Box dan Gwilym M. Jangkins. Model time series ARIMA menggunakan teknik-teknik korelasi. Identifikasi model bisa dilihat dari ACF (Autocorrelation Function) dan PACF (Partial Autocorrelation Function) suatu deret waktu. Tujuan model ARIMA dalam penelitian ini adalah untuk menemukan suatu model yang akurat yang mewakili pola masa lalu dan masa depan dari suatu data time series. Pada penelitian ini, Penulis akan menganalisis penurunan algoritma suatu metode peramalan yang disebut metode peramalan ARIMA Kemudian menerapkan metode tersebut pada data riil yaitu data produksi air di PDAM Pamekasan dengan bantuan komputer dan software SPSS, yang nantinya akan diterapkan di dalam memberikan informasi dan analisis yang akurat terhadap perusahaan PDAM Pamekasan.Dari hasil pembahasan diperoleh rumus ARIMA yang berbentuk: Profit=+Y+Z, kemudian dari hasil penerapan data riil yaitu pada data produksi air di PDAM Pamekasan diperoleh model ARIMA (1 0 0) (0 0 1) sebagai model terbaik. Dengan model : 

scholarly journals Self-Identification ResNet-ARIMA Forecasting Model

2020 ◽  
Vol 15 ◽  
Keyword(s):  
Time Series ◽  
Autocorrelation Function ◽  
Time Series Data ◽  
Moving Average ◽  
Arima Model ◽  
Model Identification ◽  
Series Data ◽  
Percentage Error ◽  
Forecasting Model ◽  
Partial Autocorrelation Function

The challenging endeavor of a time series forecast model is to predict the future time series data accurately. Traditionally, the fundamental forecasting model in time series analysis is the autoregressive integrated moving average model or the ARIMA model requiring a model identification of a three-component vector which are the autoregressive order, the differencing order, and the moving average order before fitting coefficients of the model via the Box-Jenkins method. A model identification is analyzed via the sample autocorrelation function and the sample partial autocorrelation function which are effective tools for identifying the ARMA order but it is quite difficult for analysts. Even though a likelihood based-method is presented to automate this process by varying the ARIMA order and choosing the best one with the smallest criteria, such as Akaike information criterion. Nevertheless the obtained ARIMA model may not pass the residual diagnostic test. This paper presents the residual neural network model, called the self-identification ResNet-ARIMA order model to automatically learn the ARIMA order from known ARIMA time series data via sample autocorrelation function, the sample partial autocorrelation function and differencing time series images. In this work, the training time series data are randomly simulated and checked for stationary and invertibility properties before they are used. The result order from the model is used to generate and fit the ARIMA model by the Box-Jenkins method for predicting future values. The whole process of the forecasting time series algorithm is called the self-identification ResNet-ARIMA algorithm. The performance of the residual neural network model is evaluated by Precision, Recall and F1-score and is compared with the likelihood basedmethod and ResNET50. In addition, the performance of the forecasting time series algorithm is applied to the real world datasets to ensure the reliability by mean absolute percentage error, symmetric mean absolute percentage error, mean absolute error and root mean square error and this algorithm is confirmed with the residual diagnostic checks by the Ljung-Box test. From the experimental results, the new methodologies of this research outperforms other models in terms of identifying the order and predicting the future values.

scholarly journals Modeling and Forecasting Periodic Time Series data with Fourier Autoregressive Model

2019 ◽  
pp. 1367-1373
Author(s):  
Abass I. Taiwo ◽  
Timothy Olabisi Olatayo ◽  
Adedayo Funmi Adedotun ◽  
Kazeem kehinde Adesanya
Keyword(s):  
Time Series ◽  
Autocorrelation Function ◽  
Autoregressive Model ◽  
Estimation Method ◽  
Information Criteria ◽  
Series Data ◽  
Percentage Error ◽  
Model Forecast ◽  
Modeling And Forecasting ◽  
Periodic Autocorrelation Function

Most frequently used models for modeling and forecasting periodic climatic time series do not have the capability of handling periodic variability that characterizes it. In this paper, the Fourier Autoregressive model with abilities to analyze periodic variability is implemented. From the results, FAR(1), FAR(2) and FAR(2) models were chosen based on Periodic Autocorrelation function (PeACF) and Periodic Partial Autocorrelation function (PePACF). The coefficients of the tentative model were estimated using a Discrete Fourier transform estimation method. FAR(1) models were chosen as the optimal model based on the smallest values of Periodic Akaike (PAIC) and Bayesian Information criteria (PBIC). The residual of the fitted models was diagnosed to be white noise. The in-sample forecast showed a close reflection of the original rainfall series while the out-sample forecast exhibited a continuous periodic forecast from January 2019 to December 2020 with relatively small values of Periodic Root Mean Square Error (PRMSE), Periodic Mean Absolute Error (PMAE) and Periodic Mean Absolute Percentage Error (PMAPE). The comparison of FAR(1) model forecast with AR(3), ARMA(2,1), ARIMA(2,1,1) and SARIMA( 1,1,1)(1,1,1)12 model forecast indicated that FAR(1) outperformed the other models as it exhibited a continuous periodic forecast. The continuous monthly periodic rainfall forecast indicated that there will be rapid climate change in Nigeria in the coming yearly and Nigerian Government needs to put in place plans to curtail its effects.

scholarly journals Time Series ARIMA Model for Prediction of Daily and Monthly Average Global Solar Radiation: The Case Study of Seoul, South Korea

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 240 ◽  
Author(s):  
Mohammed Alsharif ◽  
Mohammad Younes ◽  
Jeong Kim
Keyword(s):  
Time Series ◽  
Solar Radiation ◽  
South Korea ◽  
Autocorrelation Function ◽  
Moving Average ◽  
Arima Model ◽  
Sarima Model ◽  
Radiation Data ◽  
Partial Autocorrelation Function ◽  
Auto Regressive

Forecasting solar radiation has recently become the focus of numerous researchers due to the growing interest in green energy. This study aims to develop a seasonal auto-regressive integrated moving average (SARIMA) model to predict the daily and monthly solar radiation in Seoul, South Korea based on the hourly solar radiation data obtained from the Korean Meteorological Administration over 37 years (1981–2017). The goodness of fit of the model was tested against standardized residuals, the autocorrelation function, and the partial autocorrelation function for residuals. Then, model performance was compared with Monte Carlo simulations by using root mean square errors and coefficient of determination (R2) for evaluation. In addition, forecasting was conducted by using the best models with historical data on average monthly and daily solar radiation. The contributions of this study can be summarized as follows: (i) a time series SARIMA model is implemented to forecast the daily and monthly solar radiation of Seoul, South Korea in consideration of the accuracy, suitability, adequacy, and timeliness of the collected data; (ii) the reliability, accuracy, suitability, and performance of the model are investigated relative to those of established tests, standardized residual, autocorrelation function (ACF), and partial autocorrelation function (PACF), and the results are compared with those forecasted by the Monte Carlo method; and (iii) the trend of monthly solar radiation in Seoul for the coming years is analyzed and compared on the basis of the solar radiation data obtained from KMS over 37 years. The results indicate that (1,1,2) the ARIMA model can be used to represent daily solar radiation, while the seasonal ARIMA (4,1,1) of 12 lags for both auto-regressive and moving average parts can be used to represent monthly solar radiation. According to the findings, the expected average monthly solar radiation ranges from 176 to 377 Wh/m2.

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