We consider the bootstrap unit root tests based on finite order autoregressive integrated models driven by iid innovations, with or without deterministic time trends. A general methodology is developed to approximate asymptotic distributions for the models driven by integrated time series, and used to obtain asymptotic expansions for the Dickey–Fuller unit root tests. The second-order terms in ...

This paper investigates the trend in the monthly real price of oil between 1990 and 2008 with a generalized autoregressive conditional heteroskedasticity (GARCH) model. Trend and volatility are estimated jointly with the maximum likelihood estimation. There is long persistence in the variance of oil price shocks, and a GARCH unit root (GUR) test can potentially yield a significant power gain re...

We study statistical inference in quantile autoregression models when the largest autoregressive coefficient may be unity. The limiting distribution of a quantile autoregression estimator and its t-statistic is derived. The asymptotic distribution is not the conventional Dickey-Fuller distribution, but a linear combination of the Dickey-Fuller distribution and the standard normal, with the weig...

Enders and Granger provide critical values to test the null hypothesis of a unit-root against the alternative of threshold adjustment. However, in obtaining their critical values, Enders and Granger did not use a consistent estimate of the threshold nor did they use a lag-augmented data generating process. This note remedies both of these problems. The power of the test statistics using the con...

Abstract In order to study energy consumption in Iran's agricultural sector, a Genetic algorithm concept was used to calculate significant factors affecting energy consumption between 1974 and 2008. Then, durability or "stability" of variables was assessed through econometric method (Augmented Dickey-Fuller test). In addition, long-term and short-term relationships of energy consumption were es...

The conceptual inception of Purchasing Power Parity (PPP) dates back to XVI century Spain. Approximately five hundred years afterwards, economists are just beginning to arrive to a partial consensus in regard to this complex theory; hence giving way to what economist Kenneth Rogoff defined in his 1996 paper as the “Purchasing Power Parity Puzzle”. My project is based on a paper written by Angel...

In this paper we focus on two major issues that surround testing for a unit root in practice, namely: (i) uncertainty as to whether or not a linear deterministic trend is present in the data, and (ii) uncertainty as to whether the initial condition of the process is (asymptotically) negligible or not. In each case simple testing procedures are proposed with the aim of maintaining good power pro...

This paper investigates the properties of Dickey-Fuller tests for seasonally unadjusted quarterly data when deterministic seasonality is present but it is neglected in the test regression. While for the random walk case the answer is straightforward, an extensive Monte Carlo study has to be performed for more realistic processes and testing strategies. The most important conclusion is that the ...

This paper investigates the relationships between stock market indices and four macroeconomics variables, namely crude oil price (COP), money supply (M2), industrial production (IP) and inflation rate (IR) in China and India. The period covers in this study is between January 1999 to January 2009. Using the Augmented Dickey-Fuller unit root test, the underlying series are tested as non-stationa...