[Verse 1] Sarah starts her morning walk, no map to guide her way Each step she takes is random chance, left or right today But here's the twist that matters most, each move builds on the last Her starting point keeps shifting up, she can't return to past [Chorus] Random walks with unit roots, shocks that never fade Permanent effects cascade, patterns that we've made Non-stationary wandering, prices drift and roam When rho equals one exactly, data can't come home [Verse 2] Stock prices paint this picture clear, yesterday's close becomes Today's new launching platform where tomorrow's journey runs Unlike the coin that finds its mean, financial markets stray Each economic earthquake leaves cracks that always stay [Chorus] Random walks with unit roots, shocks that never fade Permanent effects cascade, patterns that we've made Non-stationary wandering, prices drift and roam When rho equals one exactly, data can't come home [Bridge] Augmented Dickey Fuller tests if roots are truly one Phillips Perron double-checks what regression work has done If p-value climbs above point-oh-five's sacred line Unit root confirmed, your series crossed the stationary line [Verse 3] White noise gets accumulated, variances explode Each period adds more chaos to this ever-growing load Forecasting becomes treacherous when trends have no anchor Spurious correlations make false relationships banker [Final Chorus] Random walks with unit roots, shocks that never fade Permanent effects cascade, patterns that we've made Non-stationary wandering, prices drift and roam When rho equals one exactly, data can't come home Data can't come home [Outro] Differencing saves the day, makes stationary what was wild Unit root transformed away, non-stationary reconciled
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