Residual-based test for Nonlinear Cointegration with application in PPPs

Nested by linear cointegration first provided in Granger (1981), the definition of nonlinear cointegration is presented in this paper. Sequentially, a nonlinear cointegrated economic system is introduced. What we mainly study is testing no nonlinear cointegration against nonlinear cointegration by residual-based test, which is ready for detecting stochastic trend in nonlinear autoregression models. We construct cointegrating regression along with smooth transition components from smooth transition autoregression model. Some properties are analyzed and discussed during the estimation procedure for cointegrating regression, including description of transition variable. Autoregression of order one is considered as the model of estimated residuals for residual-based test, from which the teststatistic is obtained. Critical values and asymptotic distribution of the test statistic that we request for different cointegrating regressions with different sample sizes are derived based on Monte Carlo simulation. The proposed theoretical methods and models are illustrated by an empirical example, comparing the results with linear cointegration application in Hamilton (1994). It is concluded that there exists nonlinear cointegration in our system in the final results.

A Note on Proxy Variables and Instrument Variable Regression

This is a note about proxy variables and instruments for identification of structural parameters in regression models. We have experienced that in the econometric textbooks these two issues are treated separately, although in practice these two concepts are very often combined. Usually, proxy variables are inserted in instrument variable regressions with the motivation they are exogenous. Implicitly meaning they are exogenous in a reduced form model and not in a structural model. Actually if these variables are exogenous they should be redundant in the structural model, e.g. IQ as a proxy for ability. Valid proxies reduce unexplained variation and increases the efficiency of the estimator of the structural parameter of interest. This is especially important in situations when the instrument is weak. With a simple example we demonstrate what is required of a proxy and an instrument when they are combined. It turns out that when a researcher has a valid instrument the requirements on the proxy variable is weaker than if no such instrument exists

Testing Seasonal Unit Roots in Data at Any Frequency, an HEGY approach

This paper generalizes the HEGY-type test to detect seasonal unit roots in data at any frequency, based on the seasonal unit root tests in univariate time series by Hylleberg, Engle, Granger and Yoo (1990). We introduce the seasonal unit roots at first, and then derive the mechanism of the HEGY-type test for data with any frequency. Thereafter we provide the asymptotic distributions of our test statistics when different test regressions are employed. We find that the F-statistics for testing conjugation unit roots have the same asymptotic distributions. Then we compute the finite-sample and asymptotic critical values for daily and hourly data by a Monte Carlo method. The power and size properties of our test for hourly data is investigated, and we find that including lag augmentations in auxiliary regression without lag elimination have the smallest size distortion and tests with seasonal dummies included in auxiliary regression have more power than the tests without seasonal dummies. At last we apply the our test to hourly wind power production data in Sweden and shows there are no seasonal unit roots in the series.

Standardisation of the Selling Process in Franchising : A Take on Sales Funnel Management

This paper addresses the two opposing extremes of standardisation in franchising and the dynamics of sales in search of a juncture point in order to reduce franchisees’ uncertainties in sales and improve sales performance. A conceptual framework is developed based on both theory and practice in order to investigate the sales process of a specific franchise network. The research is conducted over a period of six weeks in form of a customised sales report considering the sales funnel concept and performance indicators along the sales process. The received quantitative data is analysed through descriptive statistics and logistic regressions in respect to what variations in the sales process can be discovered and what practices yield higher performance. The results indicate an advantage of a prioritisation guideline regarding the activities and choices to make as a salesperson over strict standardisation. Defining the sales funnel plus engaging in the process of monitoring sales in itself has proven to be a way of reducing uncertainty as the franchisor and franchisees alike inherently gain a greater understanding of the process. The extended knowledge gained from this research allowed for both practical as well as theoretical implications and expands the knowledge on standardisation of sales and the appropriateness of the sales funnel and its management for dealing with the dilemma between standardisation and flexibility of sales in franchising contexts.

Selection and Floral Evolution in Platanthera bifolia and P. chlorantha (Orchidaceae)

Natural selection mediated by pollinators has influenced the evolution of floral diversity of the flowering plants (angiosperms). The scope of this thesis was to study: 1) phenotypic selection, 2) mating systems, and 3) floral shifts involved in plant speciation. Model plant species were Platanthera bifolia and P. chlorantha (Orchidaceae). These orchids are moth-pollinated, strictly co-sexual (bisexual flowers), and produce a spike that displays 10-20 white flowers. I explored the influence of characters on plant fitness by using multiple linear regressions. Pollen removal (male fitness) and fruit set (female fitness) increased with more flowers per plant in three P. bifolia populations. There was selection towards longer spurs in a dry year when average spur length was shorter than in normal-wet years. Female function was sensitive to drought, which enabled an application of the male function hypothesis of floral evolution (Bateman's principle). The results show that selection may vary between populations, years, and sex-functions. I examined inbreeding by estimating levels of geitonogamy (self-pollination between flowers of an individual) with an emasculation method in two P. bifolia populations. Geitonogamy did not vary with inflorescence size. Levels of geitonogamy was 20-40% in the smaller, but non-significant in the larger population. This may relate to lower number of possible mates and pollinator activity in the smaller population. Platanthera bifolia exhibits the ancestral character state of tongue-attachment of pollinia on the pollinator. Its close relative P. chlorantha attaches its pollinia onto the pollinator's eyes. To explore the mechanism of a floral shift, pollination efficiency and speed was compared between the two species. The results showed no differences in pollination efficiency, but P. chlorantha had faster pollen export and import. Efficiency of pollination in terms of speed may cause floral shifts, and thus speciation.