Research On The Seasonal Index Of Qualitative Data

In actual economy life, there often exists regular cycle variation in economic phenomena and economic activities caused by the influence of the factors such as climate conditions, production conditions, festivals and holidays, customs, and etc., the so-called seasonal variations. At present, the main research objects on seasonal variations are quantitative data, but seldom concerning qualitative data. In fact, there exist seasonal variations of qualitative data in economic activities. It has certain theoretical meaning and an extensive value in application to study on how to judge whether there exist seasonal variations of qualitative data, how to measure the degree of the seasonal variations and how to do descriptive statistics and inferential statistics research.At first, according to the relations between the proportion of qualitative data and the mean value of quantitative data, this paper defines the seasonal index of qualitative data.Then, this paper uses linear probability model to analyze seasonal variations of qualitative data. According to the needs of the research, this paper chooses the binary linear probability model of group data and do point estimation, interval estimation and hypothesis test using this model. When establishing the binary linear probability model, it discusses the model containing no long-term trend and the model containing long-term trend separately. For the model containing long-term trend, according to the properties of the long-term trend, it can be divided into linear long-term trend and non-linear long-term trend. There exist some differences of the processing method between the model containing long-term trend and the model containing no long-term trend, so this paper discuss them separately, too. And then, it applies specific examples to explain the described theory.At last, this paper proposes the method of sampling-based estimation of the seasonal index of qualitative data. Because the linear probability model requires the data to satisfy relevant hypothetic conditions, there are some restrictions of the linear probability model in actual application. However, the method of sampling-based estimation has no such requirements, under the condition of large sample, it can get the corresponding conclusions. When discussing the method of sampling-based estimation, this paper gives the general ratio estimator of seasonal index of qualitative data and the statistical properties of the estimator which are bias of the estimator, mean square error of the estimator and estimation of mean square error of the estimator, then does interval estimation and hypothesis test, proposes the method of allocation and estimation of the sample size about sampling-based estimation of the seasonal index of qualitative data.