| int __stdcall NDK_ADFTEST | ( | double * | X, |
| size_t | N, | ||
| WORD | K, | ||
| WORD | options, | ||
| BOOL | testDown, | ||
| double | alpha, | ||
| WORD | method, | ||
| WORD | retType, | ||
| double * | retVal | ||
| ) |
Returns the p-value of the Augmented Dickey-Fuller (ADF) test, which tests for a unit root in the time series sample.
- Returns
- status code of the operation
- Return values
NDK_SUCCESS Operation successful NDK_FAILED Operation unsuccessful. See Macros for full list.
- Parameters
[in] X is the univariate time series data (a one dimensional array). [in] N is the number of observations in X. [in] K is the lag length of the autoregressive process. If missing, an initial value equal to the cubic root of the input data size is used. [in] options is the model description flag for the Dickey-Fuller test variant (1=no constant, 2=contant-only, 3=trend only, 4=constant and trend, 5=const, trend and trend squared). [in] testDown is the mode of testing. If set to TRUE (default), ADFTest performs a series of tests. The test starts with the input length lag, but the actual length lag order used is obtained by testing down. [in] alpha is the statistical significance level. If missing, a default of 5% is assumed. [in] method is the statistical test to perform (1=ADF). [in] retType is a switch to select the return output: Method Value Description TEST_PVALUE 1 P-Value TEST_SCORE 2 Test statistics (aka score) TEST_CRITICALVALUE 3 Critical value. [out] retVal is the calculated test statistics.
- Remarks
- 1. The testing procedure for the ADF test is applied to the following model: \[\Delta y_t = \alpha + \beta_1 t + \beta_2 t^2 + \gamma y_{t-1} + \phi_1 \Delta y_{t-1} + \cdots + \phi_{p-1} \Delta y_{t-p+1} + \varepsilon_t\]
- Where:
- \(\Delta \) is the first different operator
- \( \alpha \) is a constant
- \( \beta_1 \) is the coefficient on a time trend
- \( \beta_2 \) is the coefficient on a squared time trend
- 2. This model can be estimated, and testing for a unit root is equivalent to testing that \(\gamma = 0\).
- 3. In sum, the Augmented Dickey-Fuller Test in Excel test hypothesis is as follows: \[H_{o}: \gamma = 0\] \[H_{1}: \gamma < 0\]
- Where:
- \(H_{o}\) is the null hypothesis (i.e. \(y_t\) has a unit-root)
- \(H_{1}\) is the alternate hypothesis (i.e. \({y_t}\) does not have a unit-root)
- 4. The test statistics (\(\tau\)) value is calculated as follows: \[\tau = \frac{\hat{\gamma}}{\sigma_{\hat\gamma}}\]
- where:
- \(\hat{\gamma}\) is the estimated coefficient
- \(\sigma_{\hat\gamma}\) is the standard error in the coefficient estimate
- 5. The test statistics value (\(\tau\)) is compared to the relevant critical value for the Dickey-Fuller Test. If the test statistic is less than the critical value, we reject the null hypothesis and conclude that no unit-root is present.
- 6. The ADFTest does not directly test for stationarity, but indirectly through the existence (or absence) of a unit-root. Furthermore, Augmented Dickey-Fuller Test in Excel incorporates a deterministic trend (and trend squared), so it allows a trend-stationary process to occur.
- 7. The main difference between the ADFTest and a normal Dickey Fuller test is that ADFTest allows for higher-order autoregressive processes.
- 8. For the test-down approach, we start with a given maximum lag length and test down by running several tests; in each, we exaimine the high-order coefficients t-stat for significance.
- 9. It is not possible to use a standard t-distribution to provide critical values for this test. Therefore this test statistic (i.e. \(\tau\)) has a specific distribution simply known as the Dickey's-Fuller table.
- 10. The time series must have at least 10, and no more than 10,000 non-missing observations.
- 11. The time series is homogeneous or equally spaced.
- 12. The time series may include missing values (e.g. NaN) at either end.
- Requirements
Header SFSDK.H Library SFSDK.LIB DLL SFSDK.DLL
- Examples
// (optional) NaN : quiet NaN (Not-A-Number) value of type double (initialization) const double NAN = std::numeric_limits<double>::quiet_NaN(); .... double data[100] = {-2.213600965,0.205653805,0.536560947,...}; WORD maxOrder=5; double alpha = 0.05; WORD method=1; double fValue = NAN; // Scenario: No deterministic component nRet = NDK_ADFTEST( data, // is the univariate time series data (a one dimensional array) 100, // is the number of observations maxOrder, // is the lag length of the autoregressive process. ADFTEST_DRIFT_ONLY, // Model 1: A stochastic drift TRUE, // is the mode of testing alpha, // is the statistical significance level 1, // is the statistical test to perform (1=ADF). TEST_PVALUE, // is a switch to select the return output &fValue // is the calculated test statistics ); if( nRet >= NDK_SUCCESS) { double fScore = NAN; double fCriticalVal = NAN; NDK_ADFTEST(data, 100, maxOrder, ADFTEST_DRIFT_ONLY, TRUE, alpha, 1, TEST_SCORE, &fValue); NDK_ADFTEST(data, 100, maxOrder, ADFTEST_DRIFT_ONLY, TRUE, alpha, 1, TEST_CRITICALVALUE, &fValue); } // Scenario 2: A deterministic constant and stochastic drift fValue = NAN; nRet = NDK_ADFTEST( data, // is the univariate time series data (a one dimensional array) 100, // is the number of observations maxOrder, // is the lag length of the autoregressive process. ADFTEST_DRIFT_N_CONST, // Model II: A deterministic constant and stochastic drift TRUE, // is the mode of testing alpha, // is the statistical significance level 1, // is the statistical test to perform (1=ADF). TEST_PVALUE, // is a switch to select the return output &fValue // is the calculated test statistics ); // Scenario 3: A deterministic trend and stochastic drift fValue = NAN; nRet = NDK_ADFTEST( data, // is the univariate time series data (a one dimensional array) 100, // is the number of observations maxOrder, // is the lag length of the autoregressive process. ADFTEST_DRIFT_N_TREND, // Model III: A deterministic trend and stochastic drift TRUE, // is the mode of testing alpha, // is the statistical significance level 1, // is the statistical test to perform (1=ADF). TEST_PVALUE, // is a switch to select the return output &fValue // is the calculated test statistics ); // Scenario 4: A deterministic constant, trend and stochastic drift fValue = NAN; nRet = NDK_ADFTEST( data, // is the univariate time series data (a one dimensional array) 100, // is the number of observations maxOrder, // is the lag length of the autoregressive process. ADFTEST_DRIFT_N_CONST_N_TREND, // Model IV: A deterministic constant, trend and stochastic drift TRUE, // is the mode of testing alpha, // is the statistical significance level 1, // is the statistical test to perform (1=ADF). TEST_PVALUE, // is a switch to select the return output &fValue // is the calculated test statistics );
| Namespace: | NumXLAPI |
| Class: | SFSDK |
| Scope: | Public |
| Lifetime: | Static |
| int NDK_ADFTEST | ( | double[] | pData, |
| UIntPtr | nSize, | ||
| UInt16 | maxOrder, | ||
| UInt16 | option, | ||
| BOOL | testDown, | ||
| double | alpha, | ||
| UInt16 | argMethod, | ||
| UInt16 | retType, | ||
| out double | retVal | ||
| ) |
Returns the p-value of the Augmented Dickey-Fuller (ADF) test, which tests for a unit root in the time series sample.
- Return Value
-
a value from NDK_RETCODE enumeration for the status of the call.
NDK_SUCCESS operation successful Error Error Code
- Parameters
[in] pData is the univariate time series data (a one dimensional array). [in] nSize is the number of observations in pData. [in] maxOrder is the lag length of the autoregressive process. If missing, an initial value equal to the cubic root of the input data size is used. [in] option is the model description flag for the Dickey-Fuller test variant (1=no constant, 2=contant-only, 3=trend only, 4=constant and trend, 5=const, trend and trend squared). [in] testDown is the mode of testing. If set to TRUE (default), ADFTest performs a series of tests. The test starts with the input length lag, but the actual length lag order used is obtained by testing down. [in] alpha is the statistical significance level. If missing, a default of 5% is assumed. [in] argMethod is the statistical test to perform (1=ADF). [in] retType is a switch to select the return output: Method Value Description TEST_PVALUE 1 P-Value TEST_SCORE 2 Test statistics (aka score) TEST_CRITICALVALUE 3 Critical value. [out] retVal is the calculated test statistics.
- Remarks
- 1. The testing procedure for the ADF test is applied to the following model: \[\Delta y_t = \alpha + \beta_1 t + \beta_2 t^2 + \gamma y_{t-1} + \phi_1 \Delta y_{t-1} + \cdots + \phi_{p-1} \Delta y_{t-p+1} + \varepsilon_t\]
- Where:
- \(\Delta \) is the first different operator
- \( \alpha \) is a constant
- \( \beta_1 \) is the coefficient on a time trend
- \( \beta_2 \) is the coefficient on a squared time trend
- 2. This model can be estimated, and testing for a unit root is equivalent to testing that \(\gamma = 0\).
- 3. In sum, the Augmented Dickey-Fuller Test in Excel test hypothesis is as follows: \[H_{o}: \gamma = 0\] \[H_{1}: \gamma < 0\]
- Where:
- \(H_{o}\) is the null hypothesis (i.e. \(y_t\) has a unit-root)
- \(H_{1}\) is the alternate hypothesis (i.e. \({y_t}\) does not have a unit-root)
- 4. The test statistics (\(\tau\)) value is calculated as follows: \[\tau = \frac{\hat{\gamma}}{\sigma_{\hat\gamma}}\]
- where:
- \(\hat{\gamma}\) is the estimated coefficient
- \(\sigma_{\hat\gamma}\) is the standard error in the coefficient estimate
- 5. The test statistics value (\(\tau\)) is compared to the relevant critical value for the Dickey-Fuller Test. If the test statistic is less than the critical value, we reject the null hypothesis and conclude that no unit-root is present.
- 6. The ADFTest does not directly test for stationarity, but indirectly through the existence (or absence) of a unit-root. Furthermore, Augmented Dickey-Fuller Test in Excel incorporates a deterministic trend (and trend squared), so it allows a trend-stationary process to occur.
- 7. The main difference between the ADFTest and a normal Dickey Fuller test is that ADFTest allows for higher-order autoregressive processes.
- 8. For the test-down approach, we start with a given maximum lag length and test down by running several tests; in each, we exaimine the high-order coefficient's t-stat for significance.
- 9. It is not possible to use a standard t-distribution to provide critical values for this test. Therefore this test statistic (i.e. \(\tau\)) has a specific distribution simply known as the Dickey's-Fuller table.
- 10. The time series must have at least 10, and no more than 10,000 non-missing observations.
- 11. The time series is homogeneous or equally spaced.
- 12. The time series may include missing values (e.g. NaN) at either end.
- Exceptions
-
Exception Type Condition None N/A
- Requirements
-
Namespace NumXLAPI Class SFSDK Scope Public Lifetime Static Package NumXLAPI.DLL
- Examples
- References
- Hull, John C.; Options, Futures and Other DerivativesFinancial Times/ Prentice Hall (2011), ISBN 978-0132777421
- Hamilton, J .D.; Time Series Analysis , Princeton University Press (1994), ISBN 0-691-04289-6
- Tsay, Ruey S.; Analysis of Financial Time Series John Wiley & SONS. (2005), ISBN 0-471-690740
