Generalized Autoregressive Conditional Heteroskedasticity Approach for Television Program Viewership Trend Analysis

Autoregressive Conditional Skewness

A number of recent studies explore how political factors influence real economic activity. With electoral models, economic performance peaks near the election, as in the retrospective model of Nordhaus [30]. Electoral cycles also emerge (at least in fiscal policy) in the rational-expectations model of Rogoff and Sibert [34] and Rogoff [33]. With partisan models, economic activity differs systematically by party, as in both the ideological model of Hibbs [26] and the rationalexpectations model of Alesina [1]. Economic activity surges after election of Democratic presidents and recedes after election of Republican presidents. Although recent tests of the electoral approach are supportive [21; 22; 24; 25], the partisan approach enjoys the more compelling support [2; 3; 9; 10; 23; 26; 27]. The electoral and partisan views are not mutually exclusive, as the possibility of conflict between ideology and the desire to be reelected as the election approaches is well recognized. Indeed, our evidence here is consistent with a combined electoralpartisan model.' The macroeconomic literature at large, however, has been slow to absorb accumulating evidence that the party affiliation of the incumbent president, together with the timing of the electoral period, are linked to real economic activity. In this study, we gauge the significance of these links for the United States and relate them to two important strands of the macroeconomic literature. One strand, the time-series literature, investigates the statistical properties of measures of real economic activity, finding that these measures often exhibit nonconstant means and heteroscedastic variances. In autoregressive, integrated, moving-average (ARIMA) models, the conditional mean is a function of past innovations, while the conditional variance is constant. Applications of ARIMA and related models, beginning with Nelson and Plosser [29], suggest that real economic activity for the United States exhibits near random-walk behavior. In autoregressive, conditional heteroscedastic (ARCH) models, the conditional variance is a function of past (squared) innovations, while the conditional mean is constant. Applications of ARCH and related models, beginning with Engle [17], suggest that real activity exhibits heteroscedastic variances.

We present a pricing kernel that summarizes well the main features of the dynamics of interest rates and risk in postwar U.S. data and use it to uncover how the pricing kernel has moved with the short rate in this data. Our findings imply that standard monetary models miss an essential link between the central bank instrument and the economic activity that monetary policy is intended to affect, and thus we call for a new approach to monetary policy analysis. We sketch a new approach using an economic model based on our pricing kernel. The model incorporates the key relationships between policy and risk movements in an unconventional way: the central bank's policy changes are viewed as primarily intended to compensate for exogenous business cycle fluctuations in risk that threaten to push inflation off target. This model, while an improvement on standard models, is considered just a starting point for their revision. It leads to critical questions that researchers need to answer as they continue to revise their approach to monetary policy analysis. Copyright © 2009 by the National Bureau of Economic Research.

We examine the relationship between the risk premium on the Center for Research on Security Prices (CRSP) value-weighted index total return and its conditional variance. We propose a new semiparametric model in which the conditional variance process is parametric and the conditional mean is an arbitrary function of the conditional variance. For monthly CRSP value-weighted excess returns, the relationship between the two moments that we uncover is nonlinear and nonmonotonic.

The purpose is to document the significance of non-linearity in the conditional mean and variance of the long-run annual UK GDP growth rate. In particular, an examination is made of asymmetry in conditional variance with respect to past shocks which implies that the conditional variance is greater, and the conditional variance function steeper, following negative shocks to output growth. Simulations of the estimated model also suggest the potential for complex dynamics including substantial amplitude changes.

In this paper we will discuss the estimation of powerline communication (PLC) asynchronous impulsive noise volatility by studying the conditional variance of the noise time series residuals. In our approach, we use the Generalized Autoregressive Conditional Heteroskedastic (GARCH) models on the basis that in our observations, the noise time series residuals indicates heteroskedasticity. By performing an ordinary least squares (OLS) regression of the noise data, the empirical results show that the conditional variance process is highly persistent in the residuals. The variance of the error terms are not uniform, in fact, the error terms are larger at some portions of the data than at other time instances. Thus, PLC impulsive noise often exhibit volatility clustering where the noise time series is comprised of periods of high volatility followed by periods of high volatility and periods of low volatility followed by periods of low volatility. The burstiness of PLC impulsive noise is therefore not spread randomly across the time period, but instead has a degree of autocorrelation. This provides evidence of time-varying conditional second order moment of the noise time series. Based on these properties, the noise time series data is said to suffer from heteroskedasticity. Numerical results provide evidence that the proposed model is capable of providing an accurate stochastic representation of the impulsive noise in the 1-30MHz frequency band. The parameter estimates of the model indicates a high degree of persistence in conditional volatility of impulsive noise which is a strong evidence of explosive volatility.

Testing Non-Linear Dependence in the Hedge Fund Industry

PurposeThe purpose of this paper is to deal with the different phases of volatility behavior and the dependence of the variability of the time series on its own past, models allowing for heteroscedasticity like autoregressive conditional heteroscedasticity (ARCH), generalized autoregressive conditional heteroscedasticity (GARCH), or regime‐switching models have been suggested by reserachers. Both types of models are widely used in practice.Design/methodology/approachBoth regime‐switching models and GARCH are used in this paper to model and explain the behavior of crude oil prices in order to forecast their volatility. In regime‐switching models, the oil return volatility has a dynamic process whose mean is subject to shifts, which is governed by a two‐state first‐order Markov process.FindingsThe GARCH models are found to be very useful in modeling a unique stochastic process with conditional variance; regime‐switching models have the advantage of dividing the observed stochastic behavior of a time series into several separate phases with different underlying stochastic processes.Originality/valueThe regime‐switching models show similar goodness‐of‐fit result to GARCH modeling, while has the advantage of capturing major events affecting the oil market. Daily data of crude oil prices are used from NYMEX Crude Oil market for the period 13 February 2006 up to 21 July 2009.

Purpose- The primary purpose of this study is to model Bitcoin price volatility and forecast its future price returns using advanced econometric models such as ARCH and GARCH. The study aims to enhance risk management strategies and support informed investment decisions by addressing the time-varying nature of Bitcoin’s volatility. The research explores the persistence of volatility shocks and the clustering of price movements to provide insights into market dynamics. Methodology- This research examines daily Bitcoin closing prices over the period from January 2020 to October 2024. The data was preprocessed to ensure reliability, including applying logarithmic transformations to standardize the data and eliminate trends. Stationarity tests, such as the Augmented Dickey-Fuller (ADF), Phillips-Perron (PP), and KPSS tests, were conducted to confirm the series' stationarity. The ARCH-LM test was utilized to detect volatility clustering which is essential for validating the use of ARCH and GARCH models. Following this, ARIMA models were employed to define mean equations and GARCH models were used to estimate conditional variance and capture volatility dynamics. The dataset was split into training and validation subsets with data from July to October 2024 reserved for validation. Findings- The findings demonstrate that Bitcoin’s price movements exhibit significant volatility clustering and persistence of shocks which are key characteristics effectively captured by ARCH and GARCH models. These models provide valuable insights into the volatility patterns of Bitcoin, supporting their application in cryptocurrency analysis. Despite their robustness, the models face limitations in precise return forecasting during highly volatile periods, suggesting the need for further refinement or integration with advanced approaches. Conclusion- The research concludes that ARCH and GARCH models are effective tools for understanding and forecasting Bitcoin’s volatility. The study underscores the importance of acknowledging volatility persistence and clustering effects when analyzing cryptocurrency price behavior. However, it also highlights areas for improvement in econometric modelling by including the exploration of hybrid models and the integration of macroeconomic factors to enhance forecasting accuracy. Keywords: Bitcoin, ARCH models, GARCH Models, forecasting, ARIMA models JEL Codes: C58, G10, G12

To be utilized in the smart charging of plug-in electric vehicles, this paper proposes semiparametric conditional mean and variance models for the daily density forecasting of the electricity load. The mean is modeled by means of an autoregressive moving average model with exogenous inputs (ARMAX), whereas several options for the variance evolution are investigated, starting with modeling the variance as a power of the conditional mean, then as a piecewise constant function, and finally as a generalized autoregressive conditional heteroskedasticity (GARCH) model. Due to the possible non-Gaussianity of the distribution of the stochastic components, a quasi-maximum likelihood estimation (QMLE) with the Pearson type IV (P-IV) distribution is also considered, apart from the estimation with the Gaussianity assumption. Moreover, the daily density forecasts are generated in a non-parametric manner by propagating samples from the stochastic components iteratively through the available model. These strategies, involving different options for variance modeling and estimation, are compared in terms of their forecast performances on two representative phase currents from the low voltage cables of medium-to-low voltage transformers in the Netherlands. The results indicate that the QMLE with the Gaussianity assumption performs better due to the additional complexity of the P-IV distribution on estimation. Concerning the variance models, the piecewise constant and GARCH models are more preferable when processing phase currents exhibiting only daily seasonality, and the model as a power of the conditional mean outperforms the others if both daily and weekly seasonality and hence more complexity is present.

In highly volatile market conditions it's always difficult to predict returns using heteroscedastic Garch models. This paper tries to investigate the impact of sample data inputs over forecast using nested conditional mean ARMAX(2,2,0) and conditional variance Garch(1,1), Gjr-garch(1,1) and Egarch(1,1) models. Research also tries to indentify relationship between outcome of formal hypothesis tests, the Ljung-Box-Pierce Q-test and Engle's ARCH test, sample input and forecast results. Study is conducted over two diversified stock markets index of America (NASDAQ Composite) and Asia (Nikkei 225). Returns are forecasted for the volatile month of aug-08 using sample inputs of last one month, two months up to seven months before aug-08 and a complete year before inputi.e from 1-aug-07 to 31-jul-08 of 246 trading days has also been taken. Graphical and correlative comparison of forecasted and observed returns is also done to identify any trend followed by Garch models in relation to size of sample inputs and forecast. Results show that forecast of mean of returns is far more accurate with Nikkei as compared to Nasdaq.

This paper attempts to model and forecast the sugar prices volatility in the India using Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models. Various types of GARCH models for instance; GARCH (1, 1), EGARCH(1, 1)were applied to sugar the period 1995–2015; to test the hypothesis of persistence, asymmetry and volatility of the spot and futuresprices. It is found that, the sum of ARCH and GARCH coefficients is not close to one, indicating that volatility shocks is not quite persistent, moreover volatility, in addition none of sugar spot and futures prices has an impact of bad news on the price volatility, while lastly leverage effect is not present on the conditional variance. Therefore (GARCH) models are appropriate in modeling and forecasting sugar prices volatility.

Two negative binomial quasi‐maximum likelihood estimates (NB‐QMLEs) for a general class of count time series models are proposed. The first one is the profile NB‐QMLE calculated while arbitrarily fixing the dispersion parameter of the negative binomial likelihood. The second one, termed two‐stage NB‐QMLE, consists of four stages estimating both conditional mean and dispersion parameters. It is shown that the two estimates are consistent and asymptotically Gaussian under mild conditions. Moreover, the two‐stage NB‐QMLE enjoys a certain asymptotic efficiency property provided that a negative binomial link function relating the conditional mean and conditional variance is specified. The proposed NB‐QMLEs are compared with the Poisson QMLE asymptotically and in finite samples for various well‐known particular classes of count time series models such as the Poisson and negative binomial integer‐valued GARCH model and the INAR(1) model. Application to a real dataset is given.

variable, given a scalar linear measurement with an additive Cauchy noise, has a conditional mean and a nite conditional variance, both being functions of the measurement. For scalar discrete linear systems with additive process and measurement noises that have Cauchy probability density functions, characteristic functions are used to generate a recursive process from which the conditional mean and variance are easily obtained. The conditional mean and variance are generated by a growing sum that at each measurement update increases by one term, constructed from four new parameters. In particular, the characteristic function of the un-normalized conditional probability density function is considered where the dynamics of the parameters are propagated by linear dynamics. These parameters are shown to decay, allowing an approximate nite dimensional recursion. Since radar measurement noise and target motion process noise are not Gaussian, but are better characterized by heavy tailed density functions, a simple homing missile problem using proportional navigation is used to demonstrate the Cauchy estimator.

Volatility is a matter of concern for time series modeling. It provides valuable insights into the fluctuation and stability of concerning variables over time. Volatility patterns in historical data can provide valuable information for predicting future behaviour. Nonlinear time series models such as the autoregressive conditional heteroscedastic (ARCH) and the generalized version of the ARCH model, i.e. generalized ARCH (GARCH) models are popularly used for capturing the volatility of a time series. The realization of any time series may have significant statistical dependencies on its distant counterpart. This phenomenon is known as the long memory process. Long memory structure can also be present in volatility. Fractionally integrated volatility models such as the fractionally integrated GARCH (FIGARCH) model can be used to capture the long memory in volatility. In this paper, we derived the out-of-sample forecast formulae along with the forecast error variances for the AR (1) -FIGARCH (1, d, 1) model by recursive use of conditional expectations and conditional variances. For empirical illustration, the modal spot prices of onion for Delhi, Lasalgaon and Bengaluru markets, India and S&P 500 index (close) data are used.