scholarly journals Revisiting linear regression of dynamical systems within the context of Zwanzig-Mori theory: tests on a simple system

2021 ◽  
Author(s):  
David Hsu ◽  
Mohsen Mazrooyisebdani ◽  
Lucas Alan Sears ◽  
Anshika Singh ◽  
Mateo N Silver ◽  
...  
Keyword(s):  
Time Series ◽  
Linear Regression ◽  
Time Series Data ◽  
Time Correlation ◽  
Harmonic Oscillators ◽  
Simple System ◽  
Series Data ◽  
Model Parameters ◽  
Mori Theory ◽  
Highly Nonlinear

<p>Linear regression can be applied to time series data to extract model parameters such as the effective force and friction constant matrices of the system. Even highly nonlinear systems can be analyzed by linear regression, if the total amount of data is broken up into shorter “time windows”, so that the dynamics is considered to be piece-wise linear. Traditionally, linear regression has been performed on the equation of motion itself (which approach we refer to as LRX). There has been surprisingly little published on the accuracy and reliability of LRX as applied to time series data. Here we show that linear regression can also be applied to the time correlation function of the dynamical observables (which approach we refer to as LRC), and that this approach is better justified within the context of statistical physics, namely, Zwanzig-Mori theory. We test LRC against LRX on a simple system of two damped harmonic oscillators driven by Gaussian random noise. We find that LRC allows one to improve the signal to noise ratio in a way that is not possible within LRX. Linear regression using time correlation functions (LRC) thus appears to be not only better justified theoretically, but it is more accurate and more versatile than LRX. <b></b></p>

scholarly journals Revisiting linear regression of dynamical systems within the context of Zwanzig-Mori theory: tests on a simple system

2021 ◽  
Author(s):  
David Hsu ◽  
Mohsen Mazrooyisebdani ◽  
Lucas Alan Sears ◽  
Anshika Singh ◽  
Mateo N Silver ◽  
...  
Keyword(s):  
Time Series ◽  
Linear Regression ◽  
Time Series Data ◽  
Time Correlation ◽  
Harmonic Oscillators ◽  
Simple System ◽  
Series Data ◽  
Model Parameters ◽  
Mori Theory ◽  
Highly Nonlinear

<p>Linear regression can be applied to time series data to extract model parameters such as the effective force and friction constant matrices of the system. Even highly nonlinear systems can be analyzed by linear regression, if the total amount of data is broken up into shorter “time windows”, so that the dynamics is considered to be piece-wise linear. Traditionally, linear regression has been performed on the equation of motion itself (which approach we refer to as LRX). There has been surprisingly little published on the accuracy and reliability of LRX as applied to time series data. Here we show that linear regression can also be applied to the time correlation function of the dynamical observables (which approach we refer to as LRC), and that this approach is better justified within the context of statistical physics, namely, Zwanzig-Mori theory. We test LRC against LRX on a simple system of two damped harmonic oscillators driven by Gaussian random noise. We find that LRC allows one to improve the signal to noise ratio in a way that is not possible within LRX. Linear regression using time correlation functions (LRC) thus appears to be not only better justified theoretically, but it is more accurate and more versatile than LRX. <b></b></p>

scholarly journals ANALISIS FAKTOR-FAKTOR YANG MEMPENGARUHI IMPOR BERAS DI INDONESIA

2019 ◽  
Vol 11 (2) ◽  
pp. 183-201
Author(s):  
Yona Namira ◽  
Iskandar Andi Nuhung ◽  
Mudatsir Najamuddin
Keyword(s):  
Time Series ◽  
Linear Regression ◽  
Multiple Linear Regression ◽  
Time Series Data ◽  
Series Data ◽  
Test Results ◽  
The Us ◽  
Rice Prices ◽  
Us Dollar ◽  
Spss Software

This study aims to 1) identify factors that affect the import of rice in Indonesia 2) analyze the influence of these factors on imports of rice in Indonesia. The data used in this research are time series data from 1994 to 2013 from the Central Statistics Agency (BPS), the Ministry of Agriculture, Ministry of Commerce, National Logistics Agency (Bulog), and Bank Indonesia. Multiple linear regression through SPSS software version 21 was employed to analyze the data. The test results together indicated the variables of productions, consumptions, stocks of rice, domestic rice prices, international rice prices and the rupiah against the US dollar affect the imports of rice in Indonesia.

scholarly journals Pengaruh Industri Sedang dan Besar Terhadap Tingkat Kemiskinan di Kabupaten Gresik Tahun 2002-2016

2021 ◽  
Vol 4 (1) ◽  
pp. 25-31
Author(s):  
Rohmatul Janah ◽  
Ida Nuraini
Keyword(s):  
Time Series ◽  
Linear Regression ◽  
Multiple Linear Regression ◽  
Time Series Data ◽  
Industrial Sector ◽  
Poverty Rate ◽  
Domestic Product ◽  
Series Data ◽  
Insignificant Effect ◽  
Poverty Levels

This research is aimed at studying the influence of medium and large industries on poverty levels in Gresik on 2002-2016. The variables used in this study is medium and large industries, a labour of medium and large industries, gross regional domestic product (GRDP) of industrial sector and poverty rate. The method used in this study used multiple linear regression and used time-series data. The results of this study simultaneously are the variables of the amount of medium and large industries, the labour medium and large industries, and the gross regional domestic product (GRDP) of the industrial sector to poverty rate is significant. While medium and large industries to poverty rate have negative and insignificant effect with a coefficient value of -0,208905. The labour of medium and large industries to poverty rate has a positive and significant effect with a coefficient value of 0,130822,  the gross regional domestic product (GRDP) of industrial to poverty rate has a negative and significant effect with a coefficient value of -0,169431.

Pengaruh pertumbuhan ekonomi, inflasi dan pengangguran terhadap tingkat kemiskinan di Sumatera Selatan

2019 ◽  
Vol 16 (1) ◽  
pp. 1-10
Author(s):  
Novegya Ratih Primandari
Keyword(s):  
Economic Growth ◽  
Time Series ◽  
Linear Regression ◽  
Linear Regression Model ◽  
Time Series Data ◽  
Secondary Data ◽  
Poverty Rate ◽  
Least Square ◽  
Series Data ◽  
Ordinary Least Square

This research aims to analyze effect of economic growth, inflation and Unemployment on the Rate of Poverty in the Province of South Sumatera. This research used secondary data in the form of time series data from 2001-2017. The method used quantitative approach by applying a linear regression model with OLS estimation Ordinary Least Square (OLS) method. The results of this study indicate that partially and simultaneously Economic Growth, Inflation and Unemployment have a significant effect on the Poverty Rate in the Province of South Sumatera.

A Novel Method to Improve the Accuracy of Grey Prediction Model in Economic Prediction

2013 ◽  
Vol 347-350 ◽  
pp. 3331-3335
Author(s):  
Qian Ru Wang ◽  
Xi Wei Chen ◽  
Da Shi Luo ◽  
Yu Feng Wei ◽  
Li Ya Jin ◽  
...  
Keyword(s):  
System Theory ◽  
Time Series Data ◽  
Grey System Theory ◽  
Series Data ◽  
Model Parameters ◽  
Economic Data ◽  
Grey System ◽  
Forecasting Accuracy ◽  
Highly Nonlinear ◽  
The Impact

Grey system theory has been widely used to forecast the economic data that are often highly nonlinear, irregular and non-stationary. Many models based on grey system theory could adapt to various economic time series data. However, some of these models didnt consider the impact of the model parameters, or only considered a simple change of the model parameters for the prediction. In this paper, we proposed the PSO based GM (1, 1) model using the optimized parameters in order to improve the forecasting accuracy. The experiment shows that PSO based GM (1, 1) gets much better forecasting accuracy compared with other widely used grey models on the actual chaotic economic data.

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.

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 PERAMALAN EKSPOR NONMIGAS DENGAN VARIASI KALENDER ISLAM MENGGUNAKAN X-13-ARIMA-SEATS (Studi Kasus: Ekspor Nonmigas Periode Januari 2013 sampai Desember 2017)

2018 ◽  
Vol 7 (3) ◽  
pp. 236-247
Author(s):  
Eka Lestari ◽  
Tatik Widiharih ◽  
Rita Rahmawati
Keyword(s):  
Time Series ◽  
Linear Regression ◽  
Foreign Exchange ◽  
Decomposition Method ◽  
Oil And Gas ◽  
Time Series Data ◽  
Series Data ◽  
Holiday Effect ◽  
Forecasting Method ◽  
Loading And Unloading

Non-oil and gas exports are one of the largest foreign exchange earners for Indonesia. Non-oil and gas exports always experience a decline in the month of Eid Al-Fitr due to delays in the delivery of export goods because the loading and unloading of goods at the port is reduced during Eid Al-Fitr. The shift of the Eid Al-Fitr month on the data will form a pattern or season with an unequal period called the moving holiday effect. The time series forecasting method that usually used the ARIMA method. Because the ARIMA method only suitable for time series data with the same seasonal period and can’t handle the moving holiday effect, the X-13-ARIMA-SEATS method used two steps. First, regARIMA modeling is a linear regression between time series data and the weight of Eid Al-Fitr and the residuals follow the ARIMA process. The weighting is based on three conditions, namely pre_holiday, post_holiday, and multiple. Second, X-12-ARIMA decomposition method for seasonal adjustments that produces trend-cycle components, seasonal, and irregular. Based on the analysis carried out on the monthly non-oil and gas export data for the period January 2013 to December 2017, the X-13-ARIMA-SEATS (1,1,0) model was obtained in the post_holiday condition as the best model. The forecasting results in 2018 show the largest decline in non-oil and gas exports in June 2018 which coincided with the Eid Al-Fitr holiday. MAPE value of 10.90% is obtained which shows that the forecasting ability is good.Keywords:  time series, non-oil and gas, X-13-ARIMA-SEATS, moving holiday

scholarly journals ANALISIS PENGARUH INFLASI, PRODUK DOMESTIK BRUTO (PDB), DAN NILAI TUKAR TERHADAP TABUNGAN MUDHARABAH PADA BANK UMUM SYARIAH (PERIODE 2013-2017)

2019 ◽  
Vol 8 (2) ◽  
pp. 138
Author(s):  
Rita Nur Wahyuningrum ◽  
Aan Zainul Anwar
Keyword(s):  
Time Series ◽  
Exchange Rate ◽  
Linear Regression ◽  
Gross Domestic Product ◽  
Multiple Linear Regression ◽  
Time Series Data ◽  
Domestic Product ◽  
Series Data ◽  
Islamic Banking ◽  
Central Statistics

<p>This study aims to analyze the effect of inflation, gross domestic product (GDP) and rupiah exchange rate on Mudharabah savings in Islamic banking in Indonesia. The data used is time series data for the period March 2013 to September 2017, which was published by Bank Indonesia from the Islamic Banking Statistics Report and the Central Statistics Agency. The technique of analyzing the research is qualitative with the method of Multiple Linear Regression. The results of this study indicate that simultaneously the Inflation, Gross Domestic Product (GDP) and Exchange Rate variables together have a significant effect on Mudharabah Savings. While partially only the Exchange Rate variable has a significant effect on Mudharabah Savings. Inflation Variables and Gross Domestic Product (GDP) have no significant effect on Mudharabah Savings.</p><p> </p><p>Keyword: inflation, gross domestic product, exchange rate, mudharabah saving</p>

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