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Create a dashboard prompt that allows case-insensitive searching on the contents of a presentation variable. The solution for this lies within the filter that is applied to the analysis and not really to anything special we do to the prompt itself. Once you have created this analysis and placed it on the dashboard, then all you need to do is to create a dashboard prompt on the page that will populate the variable, and you are ready to roll.

Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. UNIT ROOTS IN TIME SERIES MODELS Shock is usually used to describe an unexpected change in a variable or in the value of the error terms at a particular time period. 1 : explosive non-stationarity Shock to the system become more influential as time goes on.

DF TEST To simplify the computation, subtract Y t-1 from both sides of the AR(1) model; If ? =0, system has a unit root. DF TEST Applying OLS method and finding the estimator for ?, the test statistic is given by The test is a one-sided left tail test.

DF TEST 12 where W(r) denotes a standard Brownian motion (Wiener process) defined on the unit interval. DF TEST Since the normalized bias (n ? 1)( ? 1) has a well defined limiting distribution that does not depend on nuisance parameters it can also be used as a test statistic for the null hypothesis H 0 : ? = 1. DF TEST With a constant term: The test regression is and includes a constant to capture the nonzero mean under the alternative. DF TEST The test statistics t ?=1 and (n ? 1)( ? 1) are computed from the above regression. DF TEST 19 Inclusion of a constant pushes the distributions of t ?=1 and (n ? 1) ( ? 1) to the left. DF TEST With constant and trend term The test regression is and includes a constant and deterministic time trend to capture the deterministic trend under the alternative.

DF TEST This formulation is appropriate for trending time series like asset prices or the levels of macroeconomic aggregates like real GDP. DF TEST The inclusion of a constant and trend in the test regression further shifts the distributions of t ?=1 and (n ? 1)( ? 1) to the left. ADF TEST The limiting distribution of the test statistic is non-standard distribution (function of Brownian motion _ or Wiener process). Choosing the Lag Length for the ADF Test An important practical issue for the implementation of the ADF test is the specification of the lag length p. Choosing the Lag Length for the ADF Test Ng and Perron (1995) suggest the following data dependent lag length selection procedure that results in stable size of the test and minimal power loss: First, set an upper bound p ma x for p. Choosing the Lag Length for the ADF Test A useful rule of thumb for determining p max, suggested by Schwert (1989), is where [ x ] denotes the integer part of x.

ADF TEST EXAMPLE: n =54 Examine the original model and the differenced one to determine the order of AR parameters.

ADF TEST If the test statistics is positive, you can automatically decide to not reject the null hypothesis of unit root. PHILLIPS-PERRON (PP) UNIT ROOT TEST Phillips and Perron (1988) have developed a more comprehensive theory of unit root nonstationarity.

So we need to create a filter on the analysis that is able to perform the case-insensitive search within a given presentation variable.

UNIT ROOTS IN TIME SERIES MODELS Shock is usually used to describe an unexpected change in a variable or in. Under the unit root null, {Y t } is not stationary and ergodic, and the usual sample moments do not converge to fixed constants.

The hypotheses to be tested This formulation is appropriate for non-trending economic and financial series like interest rates, exchange rates and spreads. This choice allows p max to grow with the sample so that the ADF test regressions are valid if the errors follow an ARMA process with unknown order.

The limiting distribution of t ?=1 is called the Dickey-Fuller (DF) distribution and does not have a closed form representation. Under H 0 : ? = 1, ? = 0 the asymptotic distributions of these test statistics are influenced by the presence but not the coefficient values of the constant and time trend in the test regression.

If the absolute value of the t-statistic for testing the significance of the last lagged difference is greater than 1.6, then set p = p max and perform the unit root test.

It is generally believed that MA terms are present in many macroeconomic time series after differencing. The Phillips-Perron (PP) unit root tests differ from the ADF tests mainly in how they deal with serial correlation and heteroskedasticity in the errors.

Consequently, quantiles of the distribution must be computed by numerical approximation or by simulation. Many economic and financial time series have a more complicated dynamic structure than is captured by a simple AR(1) model. Said and Dickey (1984) developed an approach in which the orders of the AR and MA components in the error terms are unknown, but can be approximated by an AR( k ) process where k is large enough to allow good approximation to the unknown ARMA( p,q ) process.

In particular, where the ADF tests use a parametric autoregression to approximate the ARMA structure of the errors in the test regression, the PP tests ignore any serial correlation in the test regression. Said and Dickey (1984) augment the basic autoregressive unit root test to accommodate general ARMA( p, q ) models with unknown orders and their test is referred to as the augmented Dickey- Fuller (ADF) test.

The tests usually give the same conclusions as the ADF tests, and the calculation of the test statistics is complex.

Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. UNIT ROOTS IN TIME SERIES MODELS Shock is usually used to describe an unexpected change in a variable or in the value of the error terms at a particular time period. 1 : explosive non-stationarity Shock to the system become more influential as time goes on.

DF TEST To simplify the computation, subtract Y t-1 from both sides of the AR(1) model; If ? =0, system has a unit root. DF TEST Applying OLS method and finding the estimator for ?, the test statistic is given by The test is a one-sided left tail test.

DF TEST 12 where W(r) denotes a standard Brownian motion (Wiener process) defined on the unit interval. DF TEST Since the normalized bias (n ? 1)( ? 1) has a well defined limiting distribution that does not depend on nuisance parameters it can also be used as a test statistic for the null hypothesis H 0 : ? = 1. DF TEST With a constant term: The test regression is and includes a constant to capture the nonzero mean under the alternative. DF TEST The test statistics t ?=1 and (n ? 1)( ? 1) are computed from the above regression. DF TEST 19 Inclusion of a constant pushes the distributions of t ?=1 and (n ? 1) ( ? 1) to the left. DF TEST With constant and trend term The test regression is and includes a constant and deterministic time trend to capture the deterministic trend under the alternative.

DF TEST This formulation is appropriate for trending time series like asset prices or the levels of macroeconomic aggregates like real GDP. DF TEST The inclusion of a constant and trend in the test regression further shifts the distributions of t ?=1 and (n ? 1)( ? 1) to the left. ADF TEST The limiting distribution of the test statistic is non-standard distribution (function of Brownian motion _ or Wiener process). Choosing the Lag Length for the ADF Test An important practical issue for the implementation of the ADF test is the specification of the lag length p. Choosing the Lag Length for the ADF Test Ng and Perron (1995) suggest the following data dependent lag length selection procedure that results in stable size of the test and minimal power loss: First, set an upper bound p ma x for p. Choosing the Lag Length for the ADF Test A useful rule of thumb for determining p max, suggested by Schwert (1989), is where [ x ] denotes the integer part of x.

ADF TEST EXAMPLE: n =54 Examine the original model and the differenced one to determine the order of AR parameters.

ADF TEST If the test statistics is positive, you can automatically decide to not reject the null hypothesis of unit root. PHILLIPS-PERRON (PP) UNIT ROOT TEST Phillips and Perron (1988) have developed a more comprehensive theory of unit root nonstationarity.

So we need to create a filter on the analysis that is able to perform the case-insensitive search within a given presentation variable.

UNIT ROOTS IN TIME SERIES MODELS Shock is usually used to describe an unexpected change in a variable or in. Under the unit root null, {Y t } is not stationary and ergodic, and the usual sample moments do not converge to fixed constants.

The hypotheses to be tested This formulation is appropriate for non-trending economic and financial series like interest rates, exchange rates and spreads. This choice allows p max to grow with the sample so that the ADF test regressions are valid if the errors follow an ARMA process with unknown order.

The limiting distribution of t ?=1 is called the Dickey-Fuller (DF) distribution and does not have a closed form representation. Under H 0 : ? = 1, ? = 0 the asymptotic distributions of these test statistics are influenced by the presence but not the coefficient values of the constant and time trend in the test regression.

If the absolute value of the t-statistic for testing the significance of the last lagged difference is greater than 1.6, then set p = p max and perform the unit root test.

It is generally believed that MA terms are present in many macroeconomic time series after differencing. The Phillips-Perron (PP) unit root tests differ from the ADF tests mainly in how they deal with serial correlation and heteroskedasticity in the errors.

Consequently, quantiles of the distribution must be computed by numerical approximation or by simulation. Many economic and financial time series have a more complicated dynamic structure than is captured by a simple AR(1) model. Said and Dickey (1984) developed an approach in which the orders of the AR and MA components in the error terms are unknown, but can be approximated by an AR( k ) process where k is large enough to allow good approximation to the unknown ARMA( p,q ) process.

In particular, where the ADF tests use a parametric autoregression to approximate the ARMA structure of the errors in the test regression, the PP tests ignore any serial correlation in the test regression. Said and Dickey (1984) augment the basic autoregressive unit root test to accommodate general ARMA( p, q ) models with unknown orders and their test is referred to as the augmented Dickey- Fuller (ADF) test.

The tests usually give the same conclusions as the ADF tests, and the calculation of the test statistics is complex.

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