Electricity demand and price forecasting are key components for the market participants and system operators as precise forecasts are necessary to manage power systems effectively. However, forecasting electricity demand and prices are challenging due to their specific features, such as high frequency, volatility, long trend, nonconstant mean and variance, mean reversion, multiple seasonalities, calendar effects, and spikes/jumps. Thus, the main aim of this study is to propose models that can efficiently forecast electricity demand and prices. To this end, the time series (demand/price) is divided into two components. The first component is considered a deterministic component that includes a trend, yearly, seasonal, and weekly periodicities, calendar effects, and lagged exogenous information and is modeled by parametric and nonparametric approaches. The second component is known as a stochastic (residual) component that is estimated using univariate autoregressive (AR) and multivariate vector autoregressive (VAR) models. The estimation of these models is carried out by four different estimation methods, including ordinary least squares (O), Lasso (L), Ridge (R), and Elastic-net (E). The proposed modeling scheme is applied to Nordic electricity demand and price time series, and one-day-ahead out-of-sample forecasts are obtained for a whole year. Besides descriptive statistics, a statistical significance test is also used to evaluate the models’ forecasting accuracy. The results suggest that the proposed methodology effectively forecasts the price and demand for electricity. In addition, the choice of the estimation procedure used for both deterministic and stochastic components has a significant effect on the forecasting results. Furthermore, multivariate vector autoregressive gives superior performance compared to univariate autoregressive models.