Given a function f : X → Σ, its `-wise direct product is the function F = f ` : X` → Σ` defined by F (x1, . . . , x`) = (f(x1), . . . , f(x`)). In this paper we study the local testability of the direct product encoding (mapping f 7→ f `). Namely, given an arbitrary function F : X` → Σ`, we wish to determine how close it is to f ` for some f : X → Σ, by making the smallest possible number of ra...

This study proposes a simple, trustworthy Chow test in the presence of heteroscedasticity and autocorrelation. The is based on series autocorrelation robust variance estimator with judiciously crafted basis functions. Like classical normal linear regression, proposed employs standard F distribution as reference distribution, which justified under fixed-smoothing asymptotics. Monte Carlo simulat...