Error Correction Model

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Introduction
Exchange rates play a vital role in a county's level of trade, which is critical to every free market economies in the world. Besides, exchange rates are source of profit in forex market. For this reasons they are among the most watched, analyzed and governmentally manipulated economic measures. Therefore, it would be interesting to explore the factors of exchange rate volatility. This paper examines possible relationship between EUR/AMD and GBP/AMD exchange rates. For analyzing relationship between these two currencies we apply to co-integration and error correction model. The first part of this paper consists of literature review of the main concepts. Here we discussed autoregressive time series, covariance stationary series, mean reversion, random walks, Dickey-Fuller statistic for a unit root test. * The second part of the project contains analysis and interpretation of co-integration and error correction model between EUR/AMD and GBP/AMD exchange rates. Considering the fact, that behavior of these two currencies has been changed during the crisis, we separately discuss three time series periods: * 1999 2013

* 1999 to 2008
* 2008 to 2013.

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Autoregressive time series
A key feature of the log-linear model’s depiction of time series and a key feature of the time series in general is that current-period values are related to previous period values. For example current exchange rate of USD/EUR is related to its exchange rate in the previous period. An autoregressive model (AR) is a time series regressed on its own past values, which represents this relationship effectively. When we use this model, we can drop the normal notation of Y as the dependent variable and X as the independent variable, because we no longer have that distinction to make. Here we simply use Xt. For instance, below we use a first order autoregression for the variable Xt. Xt=b0+b1*Xt-1+εt

Covariance stationary series
To conduct valid statistical inference we must make a key assumption in time series analysis: We must assume that the time series we are modeling is Covariance Stationary. The basic idea is that a time series is covariance stationary, if its mean and variance do not change over time. A covariance stationary series must satisfy three principal requirements. * Expected value of the time series must be constant and finite in all periods. * Variance should be constant and finite.

* The covariance of the time series with itself for a fixed number of periods in the past or future must be constant and finite. So, we can summarize if the plot shows the same mean and variance through time without any significant seasonality, then the time series is covariance stationary. What happens if a time series is not covariance stationary but we use auto regression model? The estimation results will have no economic meaning. For a non-covariance- stationary time series, estimating the regression with the help of AR model will yield spurious results. Mean Reversion

We say that time series shows mean reversion if it tends to fall when its level is above its mean and rise when its level is below its mean. If a time series are currently at its mean reverting level, then the model predicts, that the value of the time series will be the same in the next period Xt+1=Xt. For an auto regressive model, the equality Xt+1 = Xt implies the level Xt = b0 + b1 * Xt or Xt = b0 / (1 - b1)

So the auto regression model predicts that time series will stay the same if its current value is b0/(1 - b1), increase if its current value is below b0 / (1 - b1), and decrease if its current value is above b0 / (1 - b1). Random Walks

A random walk is a time series in which the value of the series in one period is the value of the series in the previous period plus an unpredictable error. Xt = Xt-1 + εt, E(εt)=0, E(εt2) = σ2, E(εt, εs) = 0 if t≠s This equation means that the time series Xt...
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