scholarly journals Least Squares Estimators for Unit Root Processes with Locally Stationary Disturbance

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Junichi Hirukawa ◽  
Mako Sadakata
Keyword(s):  
Random Walk ◽  
Least Squares ◽  
Unit Root ◽  
Time Series Data ◽  
Financial Time Series ◽  
Series Data ◽  
Spectral Structure ◽  
Special Cases ◽  
Unit Root Process ◽  
Near Unit Root

The random walk is used as a model expressing equitableness and the effectiveness of various finance phenomena. Random walk is included in unit root process which is a class of nonstationary processes. Due to its nonstationarity, the least squares estimator (LSE) of random walk does not satisfy asymptotic normality. However, it is well known that the sequence of partial sum processes of random walk weakly converges to standard Brownian motion. This result is so-called functional central limit theorem (FCLT). We can derive the limiting distribution of LSE of unit root process from the FCLT result. The FCLT result has been extended to unit root process with locally stationary process (LSP) innovation. This model includes different two types of nonstationarity. Since the LSP innovation has time-varying spectral structure, it is suitable for describing the empirical financial time series data. Here we will derive the limiting distributions of LSE of unit root, near unit root and general integrated processes with LSP innovation. Testing problem between unit root and near unit root will be also discussed. Furthermore, we will suggest two kind of extensions for LSE, which include various famous estimators as special cases.

LONG MEMORY IN FINANCIAL TIME SERIES DATA WITH NON-GAUSSIAN DISTURBANCES

2003 ◽  
Vol 06 (02) ◽  
pp. 119-134 ◽  
Author(s):  
LUIS A. GIL-ALANA
Keyword(s):  
Time Series ◽  
Confidence Intervals ◽  
Unit Root ◽  
Time Series Data ◽  
Financial Time Series ◽  
Critical Values ◽  
Series Data ◽  
Finite Sample ◽  
Financial Time ◽  
Non Gaussian

In this article we propose the use of a version of the tests of Robinson [32] for testing unit and fractional roots in financial time series data. The tests have a standard null limit distribution and they are the most efficient ones in the context of Gaussian disturbances. We compute finite sample critical values based on non-Gaussian disturbances and the power properties of the tests are compared when using both, the asymptotic and the finite-sample (Gaussian and non-Gaussian) critical values. The tests are applied to the monthly structure of several stock market indexes and the results show that the if the underlying I(0) disturbances are white noise, the confidence intervals include the unit root; however, if they are autocorrelated, the unit root is rejected in favour of smaller degrees of integration. Using t-distributed critical values, the confidence intervals for the non-rejection values are generally narrower than with the asymptotic or than with the Gaussian finite-sample ones, suggesting that they may better describe the time series behaviour of the data examined.

scholarly journals An Application of the Associate Hopfield Network for Pattern Matching in Chart Analysis

2021 ◽  
Vol 11 (9) ◽  
pp. 3876
Author(s):  
Weiming Mai ◽  
Raymond S. T. Lee
Keyword(s):  
Time Series ◽  
Pattern Matching ◽  
Time Series Data ◽  
Financial Time Series ◽  
Noisy Data ◽  
Hopfield Neural Network ◽  
Hopfield Network ◽  
Series Data ◽  
Financial Time ◽  
Chart Patterns

Chart patterns are significant for financial market behavior analysis. Lots of approaches have been proposed to detect specific patterns in financial time series data, most of them can be categorized as distance-based or training-based. In this paper, we applied a trainable continuous Hopfield Neural Network for financial time series pattern matching. The Perceptually Important Points (PIP) segmentation method is used as the data preprocessing procedure to reduce the fluctuation. We conducted a synthetic data experiment on both high-level noisy data and low-level noisy data. The result shows that our proposed method outperforms the Template Based (TB) and Euclidean Distance (ED) and has an advantage over Dynamic Time Warping (DTW) in terms of the processing time. That indicates the Hopfield network has a potential advantage over other distance-based matching methods.

scholarly journals A Granger Causal Analysis of Tax-Spend Hypothesis: Evidence from Malaysia

2021 ◽  
Vol 124 ◽  
pp. 04002
Author(s):  
Hanana Khan ◽  
Maran Marimuthu ◽  
Fong-Woon Lai
Keyword(s):  
Unit Root ◽  
Budget Deficit ◽  
Time Series Data ◽  
Financial Burden ◽  
Causal Analysis ◽  
Government Expenditures ◽  
Series Data ◽  
Causality Analysis ◽  
Long Run ◽  
Short Run

In economics, the investigation of the association between government revenues (GR) and government expenditures (GE) remains an essential discussion because of its vital role in policy implication concerning the Budget deficit. This paper aims to conduct a causal analysis of these two fiscal variables (government revenue and expenditure) using financial time-series data covering the period from 1990 to 2019 of Malaysia. The analyses used the unit root, Johanson Cointegration, and the Vector Error Correction Model (VECM). Unit root test proposed tested variables are integrated at a level first. Johanson's cointegration test disclosed the fact that long-run relationships exist between the tested variable. Finally, Granger causality analysis reveals a one-way relation between government revenues and expenditures and this unidirectional association is from revenues to expenditures which indicates that in Malaysia, expenditures are supported by revenues; in other words, the Tax-spend hypothesis is supported. In VECM short-run analysis, government revenues can affect government expenditures significantly and 11% disequilibrium can be corrected in the short-run. In short-run and long-run revenues are supporting expenditures. The study recommends that to avoid a high risk of economic problems like a fiscal illusion, unnecessary financial burden, and inflation policymakers should not be imposing a high tax rate to cut the budget deficit.

scholarly journals Financial innovation and economic growth: evidence from Zimbabwe

2016 ◽  
Vol 13 (2) ◽  
pp. 65-75 ◽  
Author(s):  
Alex Bara ◽  
Calvin Mudzingiri
Keyword(s):  
Economic Growth ◽  
Developing Countries ◽  
Time Series Data ◽  
Financial Time Series ◽  
Financial Innovation ◽  
Dark Side ◽  
Series Data ◽  
Distributed Lag ◽  
Long Run ◽  
Causality Tests

The role of financial innovation on economic growth in developing countries has not been actively pursued. Stemming from the finance-growth nexus, literature suggests that financial innovation has a relationship to growth, which could be either positive or negative. Implicitly, financial innovation has a good and a dark side that affects growth. This study establishes the causal relationship between financial innovation and economic growth in Zimbabwe empirically. Using the Autoregressive Distributed Lag (ARDL) bounds tests and Granger causality tests on financial time series data of Zimbabwe for the period 1980-2013, the study finds that financial innovation has a relationship to economic growth that varies depending on the variable used to measure financial innovation. A long-run, growth-driven financial innovationis confirmed, with causality running from economic growth to financial innovation. Bi-directional causality also exists after conditionally netting-off financial development. Policies that enhance economic growth inter-twined with financial innovation are essential, if developing countries, such as Zimbabwe, aim to maximize economic development

scholarly journals Multiband Prediction Model for Financial Time Series with Multivariate Empirical Mode Decomposition

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
Md. Rabiul Islam ◽  
Md. Rashed-Al-Mahfuz ◽  
Shamim Ahmad ◽  
Md. Khademul Islam Molla
Keyword(s):  
Time Series ◽  
Empirical Mode Decomposition ◽  
Time Series Data ◽  
Financial Time Series ◽  
Arma Model ◽  
Series Data ◽  
Discrete Wavelet ◽  
Multivariate Empirical Mode Decomposition ◽  
Financial Time ◽  
Mode Decomposition

This paper presents a subband approach to financial time series prediction. Multivariate empirical mode decomposition (MEMD) is employed here for multiband representation of multichannel financial time series together. Autoregressive moving average (ARMA) model is used in prediction of individual subband of any time series data. Then all the predicted subband signals are summed up to obtain the overall prediction. The ARMA model works better for stationary signal. With multiband representation, each subband becomes a band-limited (narrow band) signal and hence better prediction is achieved. The performance of the proposed MEMD-ARMA model is compared with classical EMD, discrete wavelet transform (DWT), and with full band ARMA model in terms of signal-to-noise ratio (SNR) and mean square error (MSE) between the original and predicted time series. The simulation results show that the MEMD-ARMA-based method performs better than the other methods.

scholarly journals Long-Range Correlations and Characterization of Financial and Volcanic Time Series

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 441 ◽  
Author(s):  
Maria C. Mariani ◽  
Peter K. Asante ◽  
Md Al Masum Bhuiyan ◽  
Maria P. Beccar-Varela ◽  
Sebastian Jaroszewicz ◽  
...  
Keyword(s):  
Time Series ◽  
Long Range ◽  
Time Series Data ◽  
Financial Time Series ◽  
Seismic Station ◽  
Volcanic Eruptions ◽  
Series Data ◽  
Fluctuation Analysis ◽  
Scaling Properties ◽  
Long Range Correlations

In this study, we use the Diffusion Entropy Analysis (DEA) to analyze and detect the scaling properties of time series from both emerging and well established markets as well as volcanic eruptions recorded by a seismic station, both financial and volcanic time series data have high frequencies. The objective is to determine whether they follow a Gaussian or Lévy distribution, as well as establish the existence of long-range correlations in these time series. The results obtained from the DEA technique are compared with the Hurst R/S analysis and Detrended Fluctuation Analysis (DFA) methodologies. We conclude that these methodologies are effective in classifying the high frequency financial indices and volcanic eruption data—the financial time series can be characterized by a Lévy walk while the volcanic time series is characterized by a Lévy flight.

scholarly journals Modeling Conditional Dependence of Stock Returns Using a Copula-based GARCH Model

2017 ◽  
Vol 6 (2) ◽  
pp. 32
Author(s):  
Eun-Joo Lee ◽  
Noah Klumpe ◽  
Jonathan Vlk ◽  
Seung-Hwan Lee
Keyword(s):  
Stock Returns ◽  
Time Series Data ◽  
Financial Time Series ◽  
Garch Model ◽  
Series Data ◽  
Future Price ◽  
Investment Strategies ◽  
Volatility Clustering ◽  
Technology Stocks ◽  
Stock Portfolio

Investigating dependence structures of stocks that are related to one another should be an important consideration in managing a stock portfolio, among other investment strategies. To capture various dependence features, we employ copula to overcome the limitations of traditional linear correlations. Financial time series data is typically characterized by volatility clustering of returns that influences an estimate of a stock’s future price. To deal with the volatility and dependence of stock returns, this paper provides procedures of combining a copula with a GARCH model which leads to the construction of a multivariate distribution. Using the copula-based GARCH approach that describes the tail dependences of stock returns, we carry out Monte Carlo simulations to predict a company’s movements in the stock market. The procedures are illustrated in two technology stocks, Apple and Samsung.

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