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A multivariate, periodic and time-varying regression model for high frequency data is proposed. The dependent univariate time series is transformed into a lower frequency multivariate time series which is analysed by a periodic regression model. In the case of hourly time series, a daily 24 times 1 vector time series is constructed and a model equation for each hour is specified. The regression coefficients are allowed to differ across equations and to vary stochastically over time. Since the unrestricted model may contain too many parameters, the state space methodology is adopted and common factors in the time-varying regression coefficients are used. Signal extraction and forecasting results are presented for French national hourly electricity loads with weather and calendar variables as regressors.