现有非平稳时间序列频域因果关系检验涉及对向量误差修正模型相关系数的非线性约束，导致其应用性较差。为此，本项目将非平稳时间序列频域因果关系检验的零假设转换为对相关模型系数的线性约束，从而给出相对简单的检验步骤。具体研究有：（1）基于向量误差修正模型，定义频域因果关系测度，然后将频域因果关系检验的零假设转换为对模型系数的线性约束，从而给出检验统计量并阐明效力；（2）基于向量误差修正模型的残差序列，间接定义频域因果关系测度，然后将频域因果关系检验的零假设转换为对相关模型系数的线性约束，从而给出间接检验统计量并阐明效力；（3）当有第三个变量存在时，为了消除第三个变量的影响，定义偏相关频域因果关系测度，然后将偏相关频域因果关系检验的零假设转换为对相关模型系数的线性约束，从而给出检验统计量并阐明效力；（4）应用非平稳时间序列频域因果关系检验研究出口和产出及货币供应量、利率和产出在不同频率处的因果关系。

The existing frequency domain causality test for non-stationary time series involves non-linear restrictions on the coefficients of the vector error correction model, which restricts the application of the test. Under this background, the research program shows that the null hypothesis of the frequency domain causality test for non-stationary time series can be transformed into a set of linear restrictions on the coefficients of the vector error correction model, and thus presents a relatively simple testing procedure. The research includes: (1) based on the vector error correction model, we define the measure of the frequency domain causality. Then, we transform the null hypothesis of the frequency domain causality test into a set of linear restrictions on the coefficients of the model, and thus present the test and clarify the power of the test; (2) based on the errors of the vector error correction model, we indirectly define the measure of the frequency domain causality. Then, we transform the null hypothesis of the frequency domain causality test into a set of linear restrictions on the coefficients of the model, and thus present the test and clarify the power of the test; (3) if there is a third variable, to exclude the impact of the third variable on the frequency domain causality test, we define the partial frequency domain causality. Then, we transform the null hypothesis of the partial frequency domain causality test into a set of linear restrictions on the coefficients of the model, and thus present the test and clarify the power of the test; (4) we apply the frequency domain causality test for non-stationary time series to study the relationship between export and output as well as the relationship among the money supply, interest rate and output.