The profitability of moving average trading rules in BRICS and emerging stock markets

Technical analysis and trading systems have been widely used by practitioners in financial markets. Since some academic studies have highlighted that these tools can generate positive alphas when compared with a buy-and-hold strategy, we studied the main stocks of the BRICS and emerging markets. We considered the period from 2000 to 2015 and observed different combinations of moving average strategies and periods. The main results indicate that, for some countries, there is a combination of periods for moving averages producing better outcomes.     

On the structure of moving average processes

This paper uses Hilbert space methods to develop a rigorous proof that the sum of two uncorrelated moving average processes of order q₁ and q₂ is an MA process of order q ≦ max (q₁, q₂). The methods establish the existence of suitable random shocks for the summed process, they illuminate relationships between the coefficients of such processes and their random shocks, and they provide means for proving that the random shocks of the summed processes are normal when the shocks of the underlying processes are normal. The role of the Wold decomposition is examined in terms of multiple representations of an MA process.     

Problems with the estimation of moving average processes

As a consequence of the well-known underidentification of the moving average model unless the parameter space is restricted, Maximum Likelihood and other estimators possess properties which can pose problems for estimation when a root of the process is close to the unit circle. The behaviour of the estimators is studied both through the analytic properties of their criterion functions and by Monte Carlo simulation. Conclusions about the choice of estimator are drawn, in particular regarding the treatment of the pre-sample residuals.     

Solving DSGE models with a nonlinear moving average

We propose a nonlinear infinite moving average as an alternative to the standard state space policy function for solving nonlinear DSGE models. Perturbation of the nonlinear moving average policy function provides a direct mapping from a history of innovations to endogenous variables, decomposes the contributions from individual orders of uncertainty and nonlinearity, and enables familiar impulse response analysis in nonlinear settings. When the linear approximation is saddle stable and free of unit roots, higher order terms are likewise saddle stable and first order corrections for uncertainty are zero. We derive the third order approximation explicitly, examine the accuracy of the method using Euler equation tests, and compare with state space approximations.     

Testing for autoregressive against moving average errors in the linear regression model

This paper presents a new approach to hypotheses testing problems which are non-nested in the classical sense and which concern the covariance matrix of the disturbance vector of the linear regression model. In particular, the application of the approach to testing for AR(1) disturbances against MA(1) disturbances is explored in some detail. Practical difficulties are discussed and selected upper bounds for the test's five percent significance points are tabulated. The small sample power of four versions of the new test are compared empirically and a clear conclusion is made in regard to the best overall test.     

Hypothesis testing based on goodness-of-fit in the moving average time series model

Small sample properties of t-tests are compared with those of tests based on relative goodness- of-fit in the context of the first order moving average time series model. Monte Carlo experiments reported in the paper suggest that the actual size of these t-tests greatly exceeds theoretical large sample significance levels, while conformity of goodness-of-fit statistics to the appropriate chi-square or F-distributions is much closer. The evidence presented suggests that practitioners are well advised to employ goodness-of-fit tests as a check on results of t-tests particularly when the latter indicate ‘significance’.     

A note on the exact transformation associated with the first-order moving average process

Exact analytical expressions for the transformation that can be used to transform a generalized regression problem into a simple regression problem are available for a variety of models. Such is the case, for instance, for purely heteroscedastic models, for the first-order Markov process and for error components models. For the first-order moving average process, on the other hand, the exact transformation has not yet been produced. This gap is filled in the present note.Implications for estimation and prediction are also considered.     

Estimation and forecasting in vector autoregressive moving average models for rich datasets

We address the issue of modelling and forecasting macroeconomic variables using rich datasets by adopting the class of Vector Autoregressive Moving Average (VARMA) models. We overcome the estimation issue that arises with this class of models by implementing an iterative ordinary least squares (IOLS) estimator. We establish the consistency and asymptotic distribution of the estimator for weak and strong VARMA(p,q) models. Monte Carlo results show that IOLS is consistent and feasible for large systems, outperforming the MLE and other linear regression based efficient estimators under alternative scenarios. Our empirical application shows that VARMA models are feasible alternatives when forecasting with many predictors. We show that VARMA models outperform the AR(1), ARMA(1,1), Bayesian VAR, and factor models, considering different model dimensions.     

Estimation in the first-order moving average model through the finite autoregressive approximation: Some asymptotic results

To estimate α in the model y_t = u_t+αu_t?1, we consider a proposal by Durbin (Biometrika, 1969). It consists in fitting an autoregression of order k to the data, and deriving from there an estimate α^. The probability limit and the variance of the limiting normal distribution of α^ are presented and discussed in detail, when the sample size T → ∞, but k remains fixed. The differences between the resulting values and those corresponding to the maximum likelihood estimator are exponentially decreasing functions of k. Several modifications of the estimator are discussed and found consistent, but asymptotically inefficient.     

The informative sample size for dynamic multiple equation systems with moving average errors

Abstract  The problem considered here, is that of finding suitable conditions for dynamic economic systems that exclude the existence of observationally equivalent structures. Here observational equivalence refers to equality of distributions or first and second moments of a small finite sample from the observable process. It is shown, that under these conditions we may act as if the lagged endogenous variables are nonrandom exogenous variables, when global identifiability is investigated.     

Structural information in recursive VAR orderings

This paper investigates structural models that will permit a Cholesky decomposition of the covariance matrix of VAR residuals to identify some structural impulse response functions. Cholesky decompositions are found to be useful identification tools for the set of partially recursive structural models. A partially recursive structure is defined as any block recursive system where the equations in one block can be recursively ordered and where the structural shocks are uncorrelated. Using this class of models, we derive necessary and sufficient conditions for the moving average representation from a Cholesky decomposition to identify structure. The paper concludes by discussing implications of these results for empirical research.     

A proof of a relationship between the generalized variances for associated autoregressive and moving average processes

Summary In this paper we give a simple proof of the result that, for any integer,r, given two processes of orderr, one autoregressive and the other moving average but both with the same parameters, then the generalized variance of all ordersk2r, for the autoregressive process, is exactly equal to the infinite order generalized variance for the moving average process.     

A panel data approach to economic forecasting: The bias-corrected average forecast

In this paper, we propose a novel approach to econometric forecasting of stationary and ergodic time series within a panel-data framework. Our key element is to employ the (feasible) bias-corrected average forecast. Using panel-data sequential asymptotics we show that it is potentially superior to other techniques in several contexts. In particular, it is asymptotically equivalent to the conditional expectation, i.e., has an optimal limiting mean-squared error. We also develop a zero-mean test for the average bias and discuss the forecast-combination puzzle in small and large samples. Monte-Carlo simulations are conducted to evaluate the performance of the feasible bias-corrected average forecast in finite samples. An empirical exercise, based upon data from a well known survey is also presented. Overall, these results show promise for the feasible bias-corrected average forecast.     

A note on Balestra's (1980) approximate estimator for the first-order moving average process

An approximate procedure, based on Balestra's stated assumptions, is developed. The new method is shown to have superior performance to the approximate procedure developed by Balestra for small sample sizes when the value of the moving average parameter, C, is between zero and 0.50. For C in this region, the new method is also shown to be nearly as good as the exact procedure.     

利用改进的ARMA模型来预测供应链中的需求

本文介绍了ARMA模型的基本原理，分析了ARMA模型在市场需求预测中的不足，进行改进。并通过应用实例说明了改进的ARMA模型应用于需求预测过程的具体步骤和实施难点。     

On new variance approximations for linear models with inequality constraints

In this paper, we examine the estimation of linear models subject to inequality constraints with a special focus on new variance approximations for the estimated parameters. For models with one inequality restriction, the proposed variance formulas are exact. The variance approximations proposed in this paper can be used in regression analysis, Kalman filtering, and balancing national accounts, when inequality constraints are to be incorporated in the estimation procedure.