Sample Autocorrelation Research Articles

Instability Feature Extraction Method of Compressor Based on Sample Autocorrelation Function

The stability of aero-engine compressor is related to flight safety. Severe instability may lead to engine surge, parking or mechanical damage and even cause flight accidents. Aiming at this problem, a compressor instability feature extraction method based on sample autocorrelation function is proposed, and an autocorrelation analysis model of fluctuating pressure is established. The model is verified and analyzed by using the flight test data of an engine, which shows the feasibility of this method. It can provide technical support for real-time monitoring and quantitative evaluation of aero-engine compressor stability and improve safe flight efficiency.

Joint pulse signal detection and DOA estimation algorithm based on eigenvalue distribution of sample autocorrelation matrix

Joint pulse signal detection and DOA estimation algorithm based on eigenvalue distribution of sample autocorrelation matrix

Two New Estimators for the Autocorrelation Function Through Singular Spectrum Analysis

It is around a century that sample autocorrelation function has been introduced and used as a standard tool in time series analysis. A vast literature can be found on the statistical properties of the sample autocorrelation function. However, it has been highlighted recently that the sum of the sample autocorrelation function over the lags 1 to [Formula: see text] is −0.5 for all time series of length T. This property produces a big concern for the cases in which all available sample autocorrelations are used in the inference. This paper provides two new alternative for estimating the autocorrelation function. These estimators come from the idea of singular spectrum analysis which is a non-parametric technique for time series analysis. The paper utilizes a simulation study to illustrate the performance of the new approach. The results suggest that further improvement to the sample autocorrelation is possible and the new methods provide an attractive alternative to the classical approach.

Time Series Model to Forecast Fresh Coconut Exports from Sri Lanka

Coconut accounts for approximately 12% of all agricultural produce in Sri Lanka with the total land area under cultivation covering 409, 244 hectares ranking second to rice production. The primary regions for coconut cultivation are the Puttalam and Kurunegala districts in North-Western Province and Gampaha district in the Western Province, forming what is known as the Coconut Triangle. This region accounts for 232,270 hectares (50.94%) of the overall coconut cultivation area. The remaining coconut cultivation areas are found in the Southern Province, specifically in the districts of Galle (13,833 hectares), Matara (14,946 hectares), and Hambantota (25,837 hectares), and in non-traditional regions of the Eastern and Northern provinces. The annual coconut production varies between 2,800 to 3,000 million nuts. Having advanced knowledge of exporting coconuts offers numerous advantages to Sri Lanka, particularly in terms of establishing forward contracts with other countries. Based on secondary data of annual fresh coconut exports from 1981 to 2020 obtained from the Coconut Development Authority (CDA) of Sri Lanka, the paper developed ARIMA (2,1,0) model to forecast export. The model was selected out of three parsimonious models which were identified from the Sample Autocorrelation Function (ACF) and Partial Autocorrelation Function (PACF) of the stationary series and a comparison of significant parameters and lowest values of Akaike Information Criterion (AIC), Schwarz Bayesian Information Criterion (SBIC) and Hannan-Quinn Information Criterion (HQIC). The errors of the fitted model were found to be random and constant variance. The model was validated using 2021 and 2022 data. The percentage errors for 2021 and 2022 are 20.23% and -29.57% respectively. The predictions for 2023 and 2024 are 14696 and 15052 respectively. The model can be used effectively by the Coconut Development Authority for decision-making. However, it is suggested to develop the model further to reduce the percentage error. Keywords: ARIMA model, Forecast, Fresh Coconut Exports and Validate

Prediction and Classification Models of Wordle Data Set Based On ARMA, XGBoost

This study intends to use machine learning method to solve the problem of predicting the number of word guessing and the difficulty of word guessing in natural language. Firstly, this study smoothed the data according to the COF method. According to the images of the sample autocorrelation function and the sample partial autocorrelation function, the ARMA model is constructed and the coefficient of the AMRA model is calculated, and the number of word contest people on March 1, 2023 is predicted to drop to [18002,20622]. Second, based on the seven attributes of the word, the XGBoost classification model is used to predict the value of the first attempt, and then the XGBoost prediction model is used to predict the results of the other attempts. Eerie distribution of different attempts to {0,8.890, 17.650, 28.191, 32.451, 11.349, 1.483}. The average accuracy of the model on the test set is 79.4%.

Evolving efficiency of the BRICS markets

This paper investigates a time-varying version of weak-form market efficiency in the BRICS countries. A moving window test for sample autocorrelations is applied alongside a Kalman filter approach to recover the hidden dynamics of the market efficiency process through appropriate time-varying autoregressive models with both homoscedastic and heteroscedastic conditional variance. Monthly data cover the period from January 1995 to December 2020, which includes the 2008–2009 global financial crisis and the recent COVID-19 recession. The results reveal that all the BRICS stock markets were affected during both periods, but generally remained weak-form efficient, with the exception of China.

Bayesian structural identification using Gaussian Process discrepancy models

Bayesian model updating based on Gaussian Process (GP) models has received attention in recent years, which incorporates kernel-based GPs to provide enhanced fidelity response predictions. Although most kernel functions provide high fitting accuracy in the training data set, their out-of-sample predictions can be highly inaccurate. This paper investigates this problem by reformulating the problem on a consistent probabilistic foundation, reviewing common choices of kernel covariance functions, and proposing a new Bayesian model selection for kernel function selection, aiming to create a balance between fitting accuracy, generalizability, and model parsimony. Computational aspects are addressed via Laplace approximation and sampling techniques, providing detailed algorithms and strategies. Numerical and experimental examples are included to demonstrate the accuracy and robustness of the proposed framework. As a result, an exponential-trigonometric covariance function is characterized and justified based on the Bayesian model selection approach and observations of the sample autocorrelation function of the response discrepancies.

Features of the Earth’s seasonal hydroclimate: characterizations and comparisons across the Köppen–Geiger climates and across continents

Detailed investigations of time series features across climates, continents and variable types can progress our understanding and modelling ability of the Earth’s hydroclimate and its dynamics. They can also improve our comprehension of the climate classification systems appearing in their core. Still, such investigations for seasonal hydroclimatic temporal dependence, variability and change are currently missing from the literature. Herein, we propose and apply at the global scale a methodological framework for filling this specific gap. We analyse over 13,000 earth-observed quarterly temperature, precipitation and river flow time series. We adopt the Köppen–Geiger climate classification system and define continental-scale geographical regions for conducting upon them seasonal hydroclimatic feature summaries. The analyses rely on three sample autocorrelation features, a temporal variation feature, a spectral entropy feature, a Hurst feature, a trend strength feature and a seasonality strength feature. We find notable differences to characterize the magnitudes of these features across the various Köppen–Geiger climate classes, as well as between continental-scale geographical regions. We, therefore, deem that the consideration of the comparative summaries could be beneficial in water resources engineering contexts. Lastly, we apply explainable machine learning to compare the investigated features with respect to how informative they are in distinguishing either the main Köppen–Geiger climates or the continental-scale regions. In this regard, the sample autocorrelation, temporal variation and seasonality strength features are found to be more informative than the spectral entropy, Hurst and trend strength features at the seasonal time scale.

Uncovering Hidden Insights with Long-Memory Process Detection: An In-Depth Overview

Long-memory models are frequently used in finance and other fields to capture long-range dependence in time series data. However, correctly identifying whether a process has long memory is crucial. This paper highlights a significant limitation in using the sample autocorrelation function (ACF) to identify long-memory processes. While the ACF establishes the theoretical definition of a long-memory process, it is not possible to determine long memory by summing the sample ACFs. Hassani’s −12 theorem demonstrates that the sum of the sample ACF is always −12 for any stationary time series with any length, rendering any diagnostic or analysis procedures that include this sum open to criticism. The paper presents several cases where discrepancies between the empirical and theoretical use of a long-memory process are evident, based on real and simulated time series. It is critical to be aware of this limitation when developing models and forecasting. Accurately identifying long-memory processes is essential in producing reliable predictions and avoiding incorrect model specification.

On singular values of large dimensional lag-[formula omitted] sample auto-correlation matrices

We study the limiting behavior of singular values of a lag-τ sample auto-correlation matrix Rτϵ of large dimensional vector white noise process, the error term ϵ in the high-dimensional factor model. We establish the limiting spectral distribution (LSD) that characterizes the global spectrum of Rτϵ, and derive the limit of its largest singular value. All the asymptotic results are derived under the high-dimensional asymptotic regime where the data dimension and sample size go to infinity proportionally. Under mild assumptions, we show that the LSD of Rτϵ is the same as that of the lag-τ sample auto-covariance matrix. Based on this asymptotic equivalence, we additionally show that the largest singular value of Rτϵ converges almost surely to the right end point of the support of its LSD. Based on these results, we further propose two estimators of total number of factors with lag-τ sample auto-correlation matrices in a factor model. Our theoretical results are fully supported by numerical experiments as well.

Correlation-Based Maximal Invariant Statistic for Spectrum Sensing

In this letter, spectrum sensing for wide-sense stationary signals with temporal correlation is studied. In order to perform uniformly most powerful invariant test (UMPIT) or locally most powerful invariant test (LMPIT), the ratio of the distributions of the maximum invariant statistics is derived in closed-form using Wijsman’s theorem. This ratio shows that UMPIT can be obtained when the signal-to-noise ratio (SNR) and the normalized auto-correlation matrix of the primary user signal are both known. In addition, the LMPIT with nominal SNR (LMPIT-NSNR) and the LMPIT with improved sample auto-correlation matrix (LMPIT-ISAC) are proposed based on this ratio. LMPIT-NSNR and LMPIT-ISAC are suitable for the case where the normalized auto-correlation matrix is known and the SNR is unknown, and for the case where both the normalized auto-correlation matrix and the SNR are unknown, respectively. Simulation results show that the performance of LMPIT-NSNR is robust to the fixed nominal SNR value and can approach the performance of UMPIT, and the LMPIT-ISAC performs better than the traditional covariance-based test.

Bootstrapping the transformed goodness-of-fit test on heavy-tailed GARCH models

We study the bootstrap inference on the goodness-of-fit test for generalized autoregressive conditional heteroskedastic (GARCH) models. Note that the commonly-used portmanteau tests for model adequacy checking necessarily impose moment conditions on innovations, we hence construct the test on the sample autocorrelations of a bounded transformation of absolute residuals, which are obtained by the least absolute deviation estimation from a fitted GARCH model. Specifically, we employ the empirical distribution function of absolute residuals as the transformation. Thus the corresponding portmanteau tests are applicable for very heavy-tailed innovations with only finite fractional moments. We bootstrap both the estimation equation and sample autocorrelations of transformed residuals to approximate the test statistics. The asymptotic validity of the bootstrap procedure is established. Monte Carlo experiments compare the finite-sample performance of the proposed bootstrap-based test with other existing tests. An empirical analysis of modeling exchange rates illustrates its usefulness.

Stochastic ACF-ZCL model of time-series signals with an application to restfulness assessment

In this paper, a stochastic model of a time-series signal has been derived using the first zero-crossing lag (ZCL) of the sample autocorrelation function (ACF). For this, the order of a power law series is obtained deterministically from its ZCL. This is extended to polynomial regression models and stochastic models of time-series signals. The residuals of both the stochastic ACF-ZCL model and the conventional PACF model represent the phasic component and noise but the former follow the beta distribution more consistently. The proposed model is applied for restfulness assessment of 10-minutes long differential dermal potentials (DDP) acquired simultaneously from all 4 limbs of subjects using a specific 4-channel data acquisition system. The findings clearly show the manner in which stages of restfulness affect the features of the deterministic (or tonic) and the stochastic (or phasic) components of the stochastic ACF-ZCL model.

New practice for investors in Chinese stock market: From perspective of fractionally integrated realized GARCH model

In this paper, based on the Realized GARCH model, the fractional integration Realized GARCH model is proposed by combining long memory parameters with conditional variance and replacing the original realized measure with the realized measure obtained after daily, weekly and monthly weighting. Based on the 5-min high-frequency data of the SSE index, the fractional integration Realized GARCH model, Realized HAR GARCH model and Realized GARCH model are investigated for their fitting effect and predictive ability on market volatility, and Monte Carlo simulations are conducted from the error terms obeying normal distribution, t-distribution and chi-square distribution so as to compare the RMSE and MAE of the three types of models with respect to conditional variance. The empirical results show that the fractionally integrated Realized GARCH model is found to better capture the long-run correlation in volatility in certain intervals by comparing the theoretical and sample auto-correlation functions, while the overall predictive power of the model is better than the other two models. Finally, it provides technical support and suggestions for investors' risk control.

Behavioral learning equilibria in New Keynesian models

We introduce Behavioral Learning Equilibria (BLE) into a multivariate linear framework and apply it to New Keynesian DSGE models. In a BLE, boundedly rational agents use simple, but optimal AR(1) forecasting rules whose parameters are consistent with the observed sample mean and autocorrelation of past data. We study the BLE concept in a standard 3‐equation New Keynesian model and develop an estimation methodology for the canonical Smets and Wouters (2007) model. A horse race between Rational Expectations (REE), BLE, and constant gain learning models shows that the BLE model outperforms the REE benchmark and is competitive with constant gain learning models in terms of in‐sample and out‐of‐sample fitness. Sample‐autocorrelation learning of optimal AR(1) beliefs provides the best fit when short‐term survey data on inflation expectations are taken into account in the estimation. As a policy application, we show that optimal Taylor rules under AR(1) expectations inherit history dependence and require a lower degrees of interest rate smoothing than REE.

Jump detection in high-frequency financial data using wavelets

The presence of spikes or cusps in high-frequency return series might generate problems in terms of inference and estimation of the parameters in volatility models. For example, the presence of jumps in a time series can influence sample autocorrelations, which can cause misidentification or generate spurious ARCH effects. On the other hand, these jumps might also hide relevant heteroskedastic behavior of the dependence structure of a series, leading to identification issues and a poorer fit to a model. This paper proposes a wavelet-shrinkage method to separate out jumps in high-frequency financial series, fitting a suitable model that accounts for its stylized facts. We also perform simulation studies to assess the effectiveness of the proposed method, in addition to illustrating the effect of the jumps in time series. Lastly, we use the methodology to model real high-frequency time series of stocks traded on the Brazilian Stock Exchange and OTC and a series of cryptocurrencies trades.

On the Measurement of Cointegration Relations Between the Indicators of the Time Series of the Current Account of the Balance of Payments and GDP (On the Example of the Republic of Azerbaijan)

The article solves the problem of constructing an econometric model (based on time series of macroeconomic indicators) that reflects the relationship between changes in the current account of the balance of payments and GDP dynamics (on the example of the Republic of Azerbaijan).In order to assess the correctness of the application of mathematical and statistical methods for analyzing the impact of foreign economic activity on the final results of the country's economic activity, the constructed model was tested. So, to test the hypotheses about the normal distribution of the series, the Jarque–Bera test, the augmented Dickey–Fuller test (ADF), the Kwiatkowski–Phillips–Schmidt–Shin (KPSS) test were used, and histograms and correlograms were constructed.In the process of studying the time series of the indicators under consideration, their non-stationarity was revealed both according to the results of descriptive statistics, the Jarque–Bera test, histograms, plots of the sample autocorrelation function (ACF) and partial autocorrelation function (PACF), and according to the Dickey–Fuller test. The transition to absolute increments, that is, to the first differences, was applied. In addition, the Johansen test was performed to identify cointegration relationships. Based on its results, when comparing linear and quadratic trends with similar characteristics, a linear one was chosen, indicating the presence of a cointegration relationship. After carrying out the Trace and Maximum Eigenvalue tests, an alternative hypothesis about the presence of one cointegration vector was accepted.The results obtained allow us to conclude that the relationship between the indicators of the current account of the balance of payments and Azerbaijan's GDP is of a long-term nature. They can also serve as a basis for building an error correction model.

Surveillance and Control of Culex quinquefasciatus Using Autocidal Gravid Ovitraps.

We monitored trap captures of Culex quinquefasciatus using an interrupted time-series study to determine if autocidal gravid ovitraps (AGO traps) were useful to control the population of this mosquito species in a community in southern Puerto Rico. Data for this report came from a previous study in which we used mass trapping to control Aedes aegypti, resulting in a significant 79% reduction in numbers of this species. The AGO traps used to monitor and control Ae. aegypti also captured numerous Cx. quinquefasciatus. Culex quinquefasciatus was monitored in surveillance AGO traps from October 2011 to February 2013, followed by a mosquito control intervention from February 2013 to June 2014. Optimal captures of this mosquito occurred on the 2nd wk after the traps were set or serviced, which happened every 8 wk. Changes in collection numbers of Cx. quinquefasciatus were positively correlated with rainfall and showed oscillations every 8 wk, as revealed by sample autocorrelation analyses. Culex quinquefasciatus was attracted to and captured by AGO traps, so mass trapping caused a significant but moderate reduction of the local population (31.2%) in comparison with previous results for Ae. aegypti, possibly resulting from female mosquitoes flying in from outside of the study area and decreased attraction to the traps past the 2nd wk of trap servicing. Because Ae. aegypti and Cx. quinquefasciatus are frequently established in urban areas, mass trapping to control the former has some impact on Cx. quinquefasciatus. Control of the latter could be improved by locating and treating its aquatic habitats within and around the community.

A flexible Bayesian framework for unbiased estimation of timescales

Timescales characterize the pace of change for many dynamic processes in nature. They are usually estimated by fitting the exponential decay of data autocorrelation in the time or frequency domain. Here we show that this standard procedure often fails to recover the correct timescales due to a statistical bias arising from the finite sample size. We develop an alternative approach to estimate timescales by fitting the sample autocorrelation or power spectrum with a generative model based on a mixture of Ornstein–Uhlenbeck processes using adaptive approximate Bayesian computations. Our method accounts for finite sample size and noise in data and returns a posterior distribution of timescales that quantifies the estimation uncertainty and can be used for model selection. We demonstrate the accuracy of our method on synthetic data and illustrate its application to recordings from the primate cortex. We provide a customizable Python package that implements our framework via different generative models suitable for diverse applications.

Parameter Measurement of LFM Signal With FRI Sampling and Nuclear Norm Denoising

Measurement of linear frequency modulation (LFM) signal is significant for radar, communication, and electronic reconnaissance fields. An LFM signal is a wideband signal whose frequency varies linearly with time, and traditional measurement methods require very high sampling rates and heavy processing to estimate parameters of the LFM signal. In this article, we propose a multichannel cooperative sampling (MCS) system based on the finite rate of innovation (FRI) theory to sample and estimate the parameters of the real-valued LFM pulse sequence (LFMPS). The MCS system consists of three parts: the autocorrelation sampling structure (ACSS), the time-delayed ACSS, and the quadrature time-staggered sampling structure (QTSS). These three parts can sample the LFMPS with sub-Nyquist sampling rate, and using the subspace method in time or frequency domain, the discontinuity locations (DLs), chirp rates, and initial frequencies (IFs) of the LFMPS can be estimated with the sub-Nyquist samples, respectively. The sampling rate of the MCS system is determined by the rate of innovation of the LFMPS, instead of signal bandwidth (BW). The minimum number of samples required for parameter estimation is proven by theoretical analysis. In addition, a nuclear norm denoising algorithm is proposed based on the low-rank property of the signal subspace, which significantly improved the performance of the measurement system in the noise environment. Simulation and hardware experimental results demonstrate the effectiveness and robustness of the proposed method.