Estimation algorithm for quantized dynamic shock error models in multiplicative noise

In this paper we present an estimation algorithm for dynamic shock-error models (DSEM) given 1-bit quantized noisy measurements of the input and output. We call our algorithm the binary series estimation algorithm (BSEA). The DSEM is a particular case of a linear errors-in-variables model and has applications in econometrics and systems theory; indeed special cases of a DSEM have potential applications in speech coding and communication systems. BSEA is computationally inexpensive as it involves counting the number of occurrences of particular patterns of zeros and ones in the input and output sequences. BSEA yields consistent parameter estimates that are asymptotically normal. Simulation studies show that for moderate length observation sequences, BSEA yields satisfactory estimates of the DSEM parameters even at low signal to noise ratios