 # Modeling and Forecasting Unemployment Rate In Sweden using various Econometric Measures

### 2016

#### Abstract

Thesis: Data: This study uses Sweden’s quarterly unemployment rate data from the first quarter of 1983 to the fourth quarter of 2015, and a total of 132 observations from the OECD have been collected. The first 112 observations are used for model estimation, and the remaining 20 observations are used to evaluate the prediction performance of the model. Variables in the study Because the study uses both univariate and multivariate time series models to simulate the unemployment rate in Sweden, the study considers some additional economic variables that have a direct or indirect relationship with the unemployment rate. According to economic theory, there is a direct relationship between GDP and the unemployment rate. When the unemployment rate is higher than the natural rate, GDP will fall, and vice versa. There is also a relationship between the unemployment rate and industrial production. When the unemployment rate is at a natural rate, the potential output measures the economic productivity. In most cases, the output of production is directly proportional to the level of inputs (capital and labor). Therefore, an increase in the unemployment rate above its natural rate is related to output below its potential, and vice versa. In addition, there is an indirect relationship between the unemployment rate and the inflation rate. Therefore, in addition to a separate unemployment rate model, this study will also model it along with changes in the percentage of GDP, industrial production, and inflation rates in the previous period. 3.2. Methodology Time series can be defined as any measurement series performed at different times, and can be divided into univariate time series and multivariate time series. Univariate time series analysis uses one series. However, when people want to model and explain the influence and relationship between time series variables, multivariate time series analysis involves multiple series data sets. 3.3. TESTING STATIONARYUnit root test without structure break Before fitting a specific model to time series data, the stationarity of the series must be checked. When the mean and autocovariance of the series remain constant throughout the time series, stationarity will appear in the time series. This means that the joint statistical distribution of any set of time series variables never depends on time. Equation (1) means that y has the same finite mean value μ in the whole process, (2) requires that the autocovariance of the process does not depend on t but only depends on the time period j, and the two vectors yt and yt-j are separated of. Therefore, if the first and second moments of a process are time-invariant, then it is stable. Generally, differences may be required to achieve smoothness. Several methods have been developed to test the stationarity of the sequence. 3.3.2. Phillips-Perron (PP) TestPhillips and Perron (1988) proposed another (non-parametric) method to control serial correlation when testing unit roots. PPmethod estimates the non-augmented DF test equation (5), and modifies the t ratio of ᾳcoefficient so that the serial correlation does not affect the asymptotic distribution of the test statistics. 3.3.3 Zivot and Andrews test The Zivot and Andrews endogenous structure fracture test is a sequential test that uses a complete sample and different dummy variables for each possible fracture date. The cut-off date is selected when the t-statistic of the unit root ADF test is the smallest (most negative). Therefore, when the evidence does not support the unit root null hypothesis, the cut-off date will be selected. Zivot and Andrews conducted unit root tests under three conditions, such as structural breaks at the series level; one-time changes in the trend slope, and structural breakthroughs in the level and slope of the serial trend function. Therefore, in order to test the zero value of the unit root for an alternative to fixed structure fracture, Zivot and Andrews (1992) use the following equations corresponding to the above three conditions. The null hypothesis of the three models assumes α=0, which means that the sequence yt contains a unit root without any structural breaks, while the alternative hypothesis α<0 indicates that the sequence is a trend-stationary process with a one-time break. Unknown point in time. The Zivot and Andrews method treats each point as a potential break date (BD), and runs regressions for each possible break date in sequence. 3.4. LAG LENGTH SELECTION The choice of lag length has a strong influence on the selection model. Too little lag can lead to incorrect specification of the model, and too much lag can lead to increased errors in forecasting. Therefore, it is important to obtain the optimal hysteresis length. 3.5. Time series model This study uses both linear and non-linear univariate and multivariate time series models. It has two parts. The first part deals with the modeling and estimation of the unemployment rate; the second part involves the prediction of the unemployment rate. 3.5.1.1 Seasonal Autoregressive Integrated Moving Average Model (SARIMA) For time series of unemployment rate, seasonality may need to be considered in the ARIMA model. This process is called the seasonal process, and it drives ARIMA into the SARIMA process. The seasonal autoregressive integrated moving average (SARIMA) model is a generalized form of the ARIMA model, which considers seasonal and non-seasonal characteristic data. Similar to the ARIMA model, the predicted value is assumed to be a linear combination of past values ​​and past errors. Read Less