Detecting Singleton Review Spammers Using Semantic Similarity

Online reviews have increasingly become a very important resource for consumers when making purchases. Though it is becoming more and more difficult for people to make well-informed buying decisions without being deceived by fake reviews. Prior works on the opinion spam problem mostly considered classifying fake reviews using behavioral user patterns. They focused on prolific users who write more than a couple of reviews, discarding one-time reviewers. The number of singleton reviewers however is expected to be high for many review websites. While behavioral patterns are effective when dealing with elite users, for one-time reviewers, the review text needs to be exploited. In this paper we tackle the problem of detecting fake reviews written by the same person using multiple names, posting each review under a different name. We propose two methods to detect similar reviews and show the results generally outperform the vectorial similarity measures used in prior works. The first method extends the semantic similarity between words to the reviews level. The second method is based on topic modeling and exploits the similarity of the reviews topic distributions using two models: bag-of-words and bag-of-opinion-phrases. The experiments were conducted on reviews from three different datasets: Yelp (57K reviews), Trustpilot (9K reviews) and Ott dataset (800 reviews).Comment: 6 pages, WWW 201

Distributions of Historic Market Data -- Relaxation and Correlations

We investigate relaxation and correlations in a class of mean-reverting models for stochastic variances. We derive closed-form expressions for the correlation functions and leverage for a general form of the stochastic term. We also discuss correlation functions and leverage for three specific models -- multiplicative, Heston (Cox-Ingersoll-Ross) and combined multiplicative-Heston -- whose steady-state probability density functions are Gamma, Inverse Gamma and Beta Prime respectively, the latter two exhibiting "fat" tails. For the Heston model, we apply the eigenvalue analysis of the Fokker-Planck equation to derive the correlation function -- in agreement with the general analysis -- and to identify a series of time scales, which are observable in relaxation of cumulants on approach to the steady state. We test our findings on a very large set of historic financial markets data.Comment: 17 pages, 8 figures, 3 table

Are there Dragon Kings in the Stock Market?

We undertake a systematic study of historic market volatility spanning roughly five preceding decades. We focus specifically on the time series of realized volatility (RV) of the S&P500 index and its distribution function. As expected, the largest values of RV coincide with the largest economic upheavals of the period: Savings and Loan Crisis, Tech Bubble, Financial Crisis and Covid Pandemic. We address the question of whether these values belong to one of the three categories: Black Swans (BS), that is they lie on scale-free, power-law tails of the distribution; Dragon Kings (DK), defined as statistically significant upward deviations from BS; or Negative Dragons Kings (nDK), defined as statistically significant downward deviations from BS. In analyzing the tails of the distribution with RV > 40, we observe the appearance of "potential" DK which eventually terminate in an abrupt plunge to nDK. This phenomenon becomes more pronounced with the increase of the number of days over which the average RV is calculated -- here from daily, n=1, to "monthly," n=21. We fit the entire distribution with a modified Generalized Beta (mGB) distribution function, which terminates at a finite value of the variable but exhibits a long power-law stretch prior to that, as well as Generalized Beta Prime (GB2) distribution function, which has a power-law tail. We also fit the tails directly with a straight line on a log-log scale. In order to ascertain BS, DK or nDK behavior, all fits include their confidence intervals and p-values are evaluated for the data points to check if they can come from the respective distributions.Comment: 20 pages, 15 figue

Distributions of Historic Market Data -- Implied and Realized Volatility

We undertake a systematic comparison between implied volatility, as represented by VIX (new methodology) and VXO (old methodology), and realized volatility. We compare visually and statistically distributions of realized and implied variance (volatility squared) and study the distribution of their ratio. We find that the ratio is best fitted by heavy-tailed -- lognormal and fat-tailed (power-law) -- distributions, depending on whether preceding or concurrent month of realized variance is used. We do not find substantial difference in accuracy between VIX and VXO. Additionally, we study the variance of theoretical realized variance for Heston and multiplicative models of stochastic volatility and compare those with realized variance obtained from historic market data.Comment: 28 pages, 40 figures, 16 table