On the Sample Autocorrelation Function’s Absolute Summability

2021 ◽  
pp. 2250004
Author(s):  
Hossein Hassani ◽  
Mohammad Reza Yeganegi ◽  
Sedigheh Zamani Mehreyan ◽  
Abdolreza Sayyareh
Keyword(s):  
Time Series ◽  
Time Series Data ◽  
Absolute Summability ◽  
Stationary Time Series ◽  
Series Data ◽  
Regularity Conditions ◽  
Negative Sample ◽  
Basic Tool ◽  
Mild Conditions ◽  
Theoretical Results

The sample ACF is the most common basic tool in analyzing time-series data. This paper provides a theoretical proof that, under some regularity conditions, sample ACF of a given stationary time series is not absolutely summable. Furthermore, it shows that under some mild conditions, the number of positive and negative sample ACFs and their absolute summation tend to infinity as the length of time series increases. The theoretical results are supported by practical evidence from a simulation study.

scholarly journals IMPACT OF TRADE ON ECONOMIC GROWTH OF PAKISTAN: AN ARDL TO CO-INTEGRATION APPROACH

2016 ◽  
Vol 55 (2) ◽  
pp. 47-58
Author(s):  
Nooreen Mujahid ◽  
Azeema Begum ◽  
Muhammad Noman
Keyword(s):  
Economic Growth ◽  
Time Series ◽  
Exchange Rate ◽  
Time Series Data ◽  
Policy Option ◽  
Stationary Time Series ◽  
Series Data ◽  
Long Run ◽  
Import And Export ◽  
The Relationship

This paper explores the relationship between export growth and economic growth in the case of Pakistan by employing time series data for the period 1971- 2013. This study has incorporated variables like GDP (Gross Domestic Product) exports, imports and Foreign Direct Investment (FDI). We have applied ARDL to co-integration and Error Correction Model (ECM). The study provides the evidence of stationary time series variables, the existence of the long - run relationship between them, and the result of ECM revealed short rum equilibrium adjustment. Pakistan has many options for enhancing the export of the country. There is a dire need to minimize trade barriers and restrictions such as import and export quotas. Government of Pakistan had introduced Structural Reforms for liberalization, privatization and de-regulation which will actually shifted the trend of trade at a significant level in the end of 1980s. Low levels of interest rate can help exportable industries in which investments are needed to promote and enhance the exports. Stable exchange rate is the first and the best policy option for increasing the export and managing the imports. There is a cause and effect relationship between exchange rate and FDI. Pakistan has to immediately find the policies and processes that support logistics and facilitates trade.

scholarly journals System for Prediction of Non Stationary Time Series based on the Wavelet Radial Bases Function Neural Network Model

2018 ◽  
Vol 8 (4) ◽  
pp. 2327 ◽  
Author(s):  
Heni Kusdarwati ◽  
Samingun Handoyo
Keyword(s):  
Neural Networks ◽  
Time Series ◽  
Time Series Data ◽  
Linear Trend ◽  
Stationary Time Series ◽  
Series Data ◽  
Training Time ◽  
Stationary Time ◽  
Computation Process ◽  
Smooth Coefficients

This paper proposes and examines the performance of a hybrid model called the wavelet radial bases function neural networks (WRBFNN). The model will be compared its performance with the wavelet feed forward neural networks (WFFN model by developing a prediction or forecasting system that considers two types of input formats: input9 and input17, and also considers 4 types of non-stationary time series data. The MODWT transform is used to generate wavelet and smooth coefficients, in which several elements of both coefficients are chosen in a particular way to serve as inputs to the NN model in both RBFNN and FFNN models. The performance of both WRBFNN and WFFNN models is evaluated by using MAPE and MSE value indicators, while the computation process of the two models is compared using two indicators, many epoch, and length of training. In stationary benchmark data, all models have a performance with very high accuracy. The WRBFNN9 model is the most superior model in nonstationary data containing linear trend elements, while the WFFNN17 model performs best on non-stationary data with the non-linear trend and seasonal elements. In terms of speed in computing, the WRBFNN model is superior with a much smaller number of epochs and much shorter training time.

scholarly journals Comparison of outlier detection techniques in non-stationary time series data

2021 ◽  
Vol 27 (1) ◽  
pp. 55-60
Author(s):  
Sampson Twumasi-Ankrah ◽  
Simon Kojo Appiah ◽  
Doris Arthur ◽  
Wilhemina Adoma Pels ◽  
Jonathan Kwaku Afriyie ◽  
...  
Keyword(s):  
Time Series ◽  
Outlier Detection ◽  
Mahalanobis Distance ◽  
Time Series Data ◽  
Principal Component ◽  
Stationary Time Series ◽  
Series Data ◽  
Distance Method ◽  
Detection Techniques ◽  
Stationary Time

This study examined the performance of six outlier detection techniques using a non-stationary time series dataset. Two key issues were of interest. Scenario one was the method that could correctly detect the number of outliers introduced into the dataset whiles scenario two was to find the technique that would over detect the number of outliers introduced into the dataset, when a dataset contains only extreme maxima values, extreme minima values or both. Air passenger dataset was used with different outliers or extreme values ranging from 1 to 10 and 40. The six outlier detection techniques used in this study were Mahalanobis distance, depth-based, robust kernel-based outlier factor (RKOF), generalized dispersion, Kth nearest neighbors distance (KNND), and principal component (PC) methods. When detecting extreme maxima, the Mahalanobis and the principal component methods performed better in correctly detecting outliers in the dataset. Also, the Mahalanobis method could identify more outliers than the others, making it the "best" method for the extreme minima category. The kth nearest neighbor distance method was the "best" method for not over-detecting the number of outliers for extreme minima. However, the Mahalanobis distance and the principal component methods were the "best" performed methods for not over-detecting the number of outliers for the extreme maxima category. Therefore, the Mahalanobis outlier detection technique is recommended for detecting outlier in nonstationary time series data.

scholarly journals Tracking Poisson Parameter for Non-Stationary Discontinuous Time Series with Taylor’s Abnormal Fluctuation Scaling

Stats ◽  
2019 ◽  
Vol 2 (1) ◽  
pp. 55-69 ◽  
Author(s):  
Gen Sakoda ◽  
Hideki Takayasu ◽  
Misako Takayasu
Keyword(s):  
Time Series ◽  
Time Series Data ◽  
State Space Model ◽  
Estimation Method ◽  
Stationary Time Series ◽  
Series Data ◽  
Large Fluctuations ◽  
Taylor’S Law ◽  
Fluctuation Scaling ◽  
Poisson Parameter

We propose a parameter estimation method for non-stationary Poisson time series with the abnormal fluctuation scaling, known as Taylor’s law. By introducing the effect of Taylor’s fluctuation scaling into the State Space Model with the Particle Filter, the underlying Poisson parameter’s time evolution is estimated correctly from given non-stationary time series data with abnormally large fluctuations. We also developed a discontinuity detection method which enables tracking the Poisson parameter even for time series including sudden discontinuous jumps. As an example of application of this new general method, we analyzed Point-of-Sales data in convenience stores to estimate change of probability of purchase of commodities under fluctuating number of potential customers. The effectiveness of our method for Poisson time series with non-stationarity, large discontinuities and Taylor’s fluctuation scaling is verified by artificial and actual time series.

scholarly journals REGRESSION QUANTILES FOR TIME SERIES

2002 ◽  
Vol 18 (1) ◽  
pp. 169-192 ◽  
Author(s):  
Zongwu Cai
Keyword(s):  
Time Series ◽  
Conditional Distribution ◽  
Time Series Data ◽  
Boundary Behavior ◽  
American Statistical Association ◽  
Series Data ◽  
Regularity Conditions ◽  
Statistical Association ◽  
Additional Advantage ◽  
Regression Quantiles

In this paper we study nonparametric estimation of regression quantiles for time series data by inverting a weighted Nadaraya–Watson (WNW) estimator of conditional distribution function, which was first used by Hall, Wolff, and Yao (1999, Journal of the American Statistical Association 94, 154–163). First, under some regularity conditions, we establish the asymptotic normality and weak consistency of the WNW conditional distribution estimator for α-mixing time series at both boundary and interior points, and we show that the WNW conditional distribution estimator not only preserves the bias, variance, and, more important, automatic good boundary behavior properties of local linear “double-kernel” estimators introduced by Yu and Jones (1998, Journal of the American Statistical Association 93, 228–237), but also has the additional advantage of always being a distribution itself. Second, it is shown that under some regularity conditions, the WNW conditional quantile estimator is weakly consistent and normally distributed and that it inherits all good properties from the WNW conditional distribution estimator. A small simulation study is carried out to illustrate the performance of the estimates, and a real example is also used to demonstrate the methodology.

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