Involuntary future projections are as frequent as involuntary memories, but more positive

► We examine the frequency and valence of involuntary mental time travel (MTT). ► Involuntary future projections were as frequent as involuntary memories. ► Involuntary memories and future projections were positively biased, but the bias was stronger for future than for past MTT. ► The positivity bias varied as a function of individual differences related to negative affect and poor attentional control.