scholarly journals First-Order Random Coefficient Multinomial Autoregressive Model for Finite-Range Time Series of Counts

Symmetry ◽  
2021 ◽  
Vol 13 (12) ◽  
pp. 2271
Author(s):  
Jie Zhang ◽  
Dehui Wang ◽  
Kai Yang ◽  
Xiaogang Dong
Keyword(s):  
Time Series ◽  
Least Squares ◽  
Autoregressive Model ◽  
Time Series Data ◽  
Random Coefficient ◽  
Series Data ◽  
Model Parameters ◽  
Finite Range ◽  
First Order ◽  
Conditional Least Squares

In view of the complexity and asymmetry of finite range multi-state integer-valued time series data, we propose a first-order random coefficient multinomial autoregressive model in this paper. Basic probabilistic and statistical properties of the model are discussed. Conditional least squares (CLS) and weighted conditional least squares (WCLS) estimators of the model parameters are derived, and their asymptotic properties are established. In simulation studies, we compare these two methods with the conditional maximum likelihood (CML) method to verify the proposed procedure. A real example is applied to illustrate the advantages of our model.

Time Series Regression with Mixtures of Integrated Processes

1995 ◽  
Vol 11 (5) ◽  
pp. 1033-1094 ◽  
Author(s):  
Yoosoon Chang ◽  
Peter C.B. Phillips
Keyword(s):  
Time Series ◽  
Least Squares ◽  
Time Series Data ◽  
Unit Roots ◽  
Ordinary Least Squares ◽  
Series Data ◽  
Vector Autoregressions ◽  
Time Series Regression ◽  
First Order ◽  
Unknown Mixture

The paper develops a statistical theory for regressions with integrated regressors of unknown order and unknown cointegrating dimension. In practice, we are often unsure whether unit roots or cointegration is present in time series data, and we are also uncertain about the order of integration in some cases. This paper addresses issues of estimation and inference in cases of such uncertainty. Phillips (1995, Econometrica 63, 1023–1078) developed a theory for time series regressions with an unknown mixture of 1(0) and 1(1) variables and established that the method of fully modified ordinary least squares (FM-OLS) is applicable to models (including vector autoregressions) with some unit roots and unknown cointegrating rank. This paper extends these results to models that contain some I(0), I(1), and I(2) regressors. The theory and methods here are applicable to cointegrating regressions that include unknown numbers of I(0), I(1), and I(2) variables and an unknown degree of cointegration. Such models require a somewhat different approach than that of Phillips (1995). The paper proposes a residual-based fully modified ordinary least-squares (RBFMOLS) procedure, which employs residuals from a first-order autoregression of the first differences of the entire regressor set in the construction of the FMOLS estimator. The asymptotic theory for the RBFM-OLS estimator is developed and is shown to be normal for all the stationary coefficients and mixed normal for all the nonstationary coefficients. Under Gaussian assumptions, estimation of the cointegration space by RBFM-OLS is optimal even though the dimension of the space is unknown.

scholarly journals Time Series Modeling on Monthly Data of Tourist Arrivals in Nepal: An Alternative Approach

2017 ◽  
Vol 1 ◽  
pp. 41-54 ◽  
Author(s):  
Amrit Subedi
Keyword(s):  
Time Series ◽  
Autoregressive Model ◽  
Time Series Data ◽  
Polynomial Function ◽  
Seasonal Fluctuation ◽  
Ar Model ◽  
Series Data ◽  
Monthly Data ◽  
Annual Trend ◽  
Alternative Approach

Background: There are various approaches of modeling on time series data. Most of the studies conducted regarding time series data are based on annual trend whereas very few concerned with data having monthly fluctuation. The data of tourist arrivals is an example of time series data with monthly fluctuation which reveals that there is higher number of tourist arrivals in some months/seasons whereas others have less number. Starting from January, it makes a complete cycle in every 12 months with 3 bends indicating that it can be captured by biquadratic function.Objective: To provide an alternative approach of modeling i.e. combination of Autoregressive model with polynomial (biquadratic) function on time series data with monthly/seasonal fluctuation and compare its adequacy with widely used cyclic autoregressive model i.e. AR (12).Materials and Methods: This study is based on monthly data of tourist arrivals in Nepal. Firstly, usual time series model AR (12) has been adopted and an alternative approach of modeling has been attempted combining AR and biquadratic function. The first part of the model i.e. AR represents annual trend whereas biquadratic part does for monthly fluctuation.Results: The fitted cyclic autoregressive model on monthly data of tourist arrivals is Est. Ym = 3614.33 + 0.9509Ym-12, (R2=0.80); Est. Ym indicates predicted tourist arrivals for mth month and Ym-12 indicates observed tourist arrivals in (m-12)th month and the combined model of AR and biquadratic function is Est. Yt(m) = -46464.6 + 1.000Yt-1 + 52911.56m - 17177m2 + 2043.95m3 - 79.43m4, (R2=0.78); Est. Yt(m) indicates predicted tourist arrivals for mth month of tth year and Yt-1 indicates average tourist arrivals in (t-1)th year. The AR model combined with polynomial function reveals normal and homoscedastic residuals more accurately compared to first one.Conclusion: The use of polynomial function combined with autoregressive model can be useful for time series data having seasonal fluctuation. It can be an alternative approach for picking up a good model for such type of data. Nepalese Journal of Statistics, 2017,  Vol. 1, 41-54

Cosinor Analysis for Temperature Time Series Data of Long Duration

2007 ◽  
Vol 9 (1) ◽  
pp. 30-41 ◽  
Author(s):  
Nikhil S. Padhye ◽  
Sandra K. Hanneman
Keyword(s):  
Time Series ◽  
Time Series Data ◽  
Model Fit ◽  
Series Data ◽  
Model Parameters ◽  
Cosinor Analysis ◽  
Long Time ◽  
Improved Model ◽  
Data Length ◽  
Cosinor Models

The application of cosinor models to long time series requires special attention. With increasing length of the time series, the presence of noise and drifts in rhythm parameters from cycle to cycle lead to rapid deterioration of cosinor models. The sensitivity of amplitude and model-fit to the data length is demonstrated for body temperature data from ambulatory menstrual cycling and menopausal women and from ambulatory male swine. It follows that amplitude comparisons between studies cannot be made independent of consideration of the data length. Cosinor analysis may be carried out on serial-sections of the series for improved model-fit and for tracking changes in rhythm parameters. Noise and drift reduction can also be achieved by folding the series onto a single cycle, which leads to substantial gains in the model-fit but lowers the amplitude. Central values of model parameters are negligibly changed by consideration of the autoregressive nature of residuals.

Correlation analysis of continuous emotional response to music: Correcting for the effects of serial correlation

2001 ◽  
Vol 5 (1_suppl) ◽  
pp. 213-236 ◽  
Author(s):  
Emery Schubert
Keyword(s):  
Time Series ◽  
Correlation Analysis ◽  
Emotional Response ◽  
Serial Correlation ◽  
Time Series Data ◽  
Second Order ◽  
Series Data ◽  
First Order ◽  
The Relationship ◽  
Pearson Correlations

Publications of research concerning continuous emotional responses to music are increasing. The developing interest brings with it a need to understand the problems associated with the analysis of time series data. This article investigates growing concern in the use of conventional Pearson correlations for comparing time series data. Using continuous data collected in response to selected pieces of music, with two emotional dimensions for each piece, two falsification studies were conducted. The first study consisted of a factor analysis of the individual responses using the original data set and its first-order differenced transformation. The differenced data aligned according to theoretical constraints better than the untransformed data, supporting the use of first-order difference transformations. Using a similar method, the second study specifically investigated the relationship between Pearson correlations, difference transformations and the critical correlation coefficient above which the conventional correlation analysis remains internally valid. A falsification table was formulated and quantified through a hypothesis index function. The study revealed that correlations of undifferenced data must be greater than 0.75 for a valid interpretation of the relationship between bivariate emotional response time series data. First and second-order transformations were also investigated and found to be valid for correlation coefficients as low as 0.24. Of the three version of the data (untransformed, first-order differenced, and second-order differenced), first-order differenced data produced the fewest problems with serial correlation, whilst remaining a simple and meaningful transformation.

scholarly journals Pemodelan Harga Beras di Pulau Sumatera dengan Menggunakan Model Generalized Space Time ARIMA

2018 ◽  
Vol 2 (2) ◽  
pp. 49-57
Author(s):  
Dwi Yulianti ◽  
I Made Sumertajaya ◽  
Itasia Dina Sulvianti
Keyword(s):  
Time Series ◽  
Time Series Data ◽  
Moving Average ◽  
Space Time ◽  
Series Data ◽  
Model Parameters ◽  
Autoregressive Integrated Moving Average ◽  
Sumatra Island ◽  
Rice Price ◽  
Multiple Variables

Generalized space time autoregressive integrated  moving average (GSTARIMA) model is a time series model of multiple variables with spatial and time linkages (space time). GSTARIMA model is an extension of the space time autoregressive integrated moving average (STARIMA) model with the assumption that each location has unique model parameters, thus GSTARIMA model is more flexible than STARIMA model. The purposes of this research are to determine the best model and predict the time series data of rice price on all provincial capitals of Sumatra island using GSTARIMA model. This research used weekly data of rice price on all provincial capitals of Sumatra island from January 2010 to December 2017. The spatial weights used in this research are the inverse distance and queen contiguity. The modeling result shows that the best model is GSTARIMA (1,1,0) with queen contiguity weighted matrix and has the smallest MAPE value of 1.17817 %.

scholarly journals Did an Ebola outbreak influence the 2014 U.S. federal elections? (Hint: Only if you ignore autocorrelation)

2016 ◽  
Author(s):  
Leonid Tiokhin ◽  
Daniel Hruschka
Keyword(s):  
Time Series ◽  
Data Analysis ◽  
Time Series Data ◽  
Series Data ◽  
Online Search ◽  
First Order ◽  
Search Volume ◽  
Temporal Autocorrelation ◽  
Analytical Strategies ◽  
Existing Data

In a recent paper, Beall, Hofer, and Schaller (2016) use observational time series data to test the hypothesis that the 2014 Ebola outbreak influenced the 2014 U.S. Federal Elections. They find substantial associations between online search volume for Ebola and people’s tendency to vote Republican, an effect observed primarily in states with norms favoring Republican candidates. However, the analyses do not deal with the well-known problem of temporal autocorrelation in time series. We show that all variables analyzed exhibit extremely high levels of temporal autocorrelation (i.e. similarity in data-point values across time). After appropriately removing first-order autocorrelation, the observed relationships are attenuated and non-significant. This suggests that either no real associations exist, or that existing data are insufficiently powered to test the proposed hypotheses. We conclude by highlighting other pitfalls of observational data analysis, and draw attention to analytical strategies developed in related disciplines for avoiding these errors.

scholarly journals Did an Ebola outbreak influence the 2014 U.S. federal elections? (Hint: Only if you ignore autocorrelation)

2016 ◽  
Author(s):  
Leonid Tiokhin ◽  
Daniel Hruschka
Keyword(s):  
Time Series ◽  
Data Analysis ◽  
Time Series Data ◽  
Series Data ◽  
Online Search ◽  
First Order ◽  
Search Volume ◽  
Temporal Autocorrelation ◽  
Analytical Strategies ◽  
Existing Data

In a recent paper, Beall, Hofer, and Schaller (2016) use observational time series data to test the hypothesis that the 2014 Ebola outbreak influenced the 2014 U.S. Federal Elections. They find substantial associations between online search volume for Ebola and people’s tendency to vote Republican, an effect observed primarily in states with norms favoring Republican candidates. However, the analyses do not deal with the well-known problem of temporal autocorrelation in time series. We show that all variables analyzed exhibit extremely high levels of temporal autocorrelation (i.e. similarity in data-point values across time). After appropriately removing first-order autocorrelation, the observed relationships are attenuated and non-significant. This suggests that either no real associations exist, or that existing data are insufficiently powered to test the proposed hypotheses. We conclude by highlighting other pitfalls of observational data analysis, and draw attention to analytical strategies developed in related disciplines for avoiding these errors.

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