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We propose an algorithm to impute and forecast a time series by transforming the observed time series into a matrix, utilizing matrix estimation to recover missing values and denoise observed entries, and performing linear regression to make predictions. At the core of our analysis is a representation result, which states that for a large class of models, the transformed time series matrix is (approximately) lowrank. In effect, this generalizes the widely used Singular Spectrum Analysis (SSA) in the time series literature, and allows us to establish a rigorous link between time series analysis and matrix estimation. The key to establishing this link is constructing a Page matrix with nonoverlapping entries rather than a Hankel matrix as is commonly done in the literature (e.g., SSA). This particular matrix structure allows us to provide finite sample analysis for imputation and prediction, and prove the asymptotic consistency of our method. Another salient feature of our algorithm is that it is model agnostic with respect to both the underlying time dynamics and the noise distribution in the observations. The noise agnostic property of our approach allows us to recover the latent states when only given access to noisy and partial observations a la amore »

We propose an algorithm to impute and forecast a time series by transforming the observed time series into a matrix, utilizing matrix estimation to recover missing values and denoise observed entries, and performing linear regression to make predictions. At the core of our analysis is a representation result, which states that for a large class of models, the transformed time series matrix is (approximately) lowrank. In effect, this generalizes the widely used Singular Spectrum Analysis (SSA) in the time series literature, and allows us to establish a rigorous link between time series analysis and matrix estimation. The key to establishing this link is constructing a Page matrix with nonoverlapping entries rather than a Hankel matrix as is commonly done in the literature (e.g., SSA). This particular matrix structure allows us to provide finite sample analysis for imputation and prediction, and prove the asymptotic consistency of our method. Another salient feature of our algorithm is that it is model agnostic with respect to both the underlying time dynamics and the noise distribution in the observations. The noise agnostic property of our approach allows us to recover the latent states when only given access to noisy and partial observations a la amore »