Graphical Representation: Graphics We Live By (Part III: Exchange Rates in Power BI)

Graphical Representation Series

An exchange rate (XR) is the rate at which one currency will be exchanged for another currency, and thus XRs are used in everything related to trades, several processes in Finance relying on them. There are various sources for the XR like the European Central Bank (ECB) that provide the row data and various analyses including graphical representations varying in complexity. Conversely, XRs' processing offers some opportunities for learning techniques for data visualization. 

On ECB there are monthly, yearly, daily and biannually XRs from EUR to the various currencies which by triangulation allow to create XRs for any of the currencies involved. If N currencies are involved for one time unit in the process (e.g. N-1 XRs) , the triangulation generates NxN values for only one time division, the result being tedious to navigate. A matrix like the one below facilitates identifying the value between any of the currencies:

The table needs to be multiplied by 12, the number of months, respectively by the number of years, and filter allowing to navigate the data as needed. For many operations is just needed to look use the EX for a given time division. There are however operations in which is needed to have a deeper understanding of one or more XR's evolution over time (e.g. GBP to NOK). 

Moreover, for some operations is enough to work with two decimals, while for others one needs to use up to 6 or even more decimals for each XR. Occasionally, one can compromise and use 3 decimals, which should be enough for most of the scenarios. Making sense of such numbers is not easy for most of us, especially when is needed to compare at first sight values across multiple columns. Summary tables can help:

Statistics like Min. (minimum), Max. (maximum), Max. - Min. (range), Avg. (average) or even StdDev. (standard deviation) can provide some basis for further analysis, while sparklines are ideal for showing trends over a time interval (e.g. months).

Usually, a heatmap helps to some degree to navigate the data, especially when there's a plot associated with it:

In this case filtering by column in the heatmap allows to see how an XR changed for the same month over the years, while the trendline allows to identify the overall tendency (which is sensitive to the number of years considered). Showing tendencies or patterns for the same month over several years complements the yearly perspective shown via sparklines.

Fortunately, there are techniques to reduce the representational complexity of such numbers. For example, one can use as basis the XRs for January (see Base Jan), and represent the other XRs only as differences from the respective XR. Thus, in the below table for February is shown the XR difference between February and January (13.32-13.22=0.10). The column for January is zero and could be omitted, though it can still be useful in further calculations (e.g. in the calculation of averages) based on the respective data..

This technique works when the variations are relatively small (e.g. the values vary around 0). The above plots show the respective differences for the whole year, respectively only for four months. Given a bigger sequence (e.g. 24, 28 months) one can attempt to use the same technique, though there's a point beyond which it becomes difficult to make sense of the results. One can also use the year end XR or even the yearly average for the same, though it adds unnecessary complexity to the calculations when the values for the whole year aren't available. 

Usually, it's recommended to show only 3-5 series in a plot, as one can better distinguish the trends. However, plotting all series allows to grasp the overall pattern, if any. Thus, in the first plot is not important to identify the individual series but to see their tendencies. The two perspectives can be aggregated into one plot obtained by applying different filtering. 

Of course, a similar perspective can be obtained by looking at the whole XRs:

The Max.-Min. and StdDev (standard deviation for population) between the last and previous tables must match. 

Certain operations require comparing the trends of two currencies. The first plot shows the evolution NOK and SEK in respect to EUR, while the second shows only the differences between the two XRs:

The first plot will show different values when performed against other currency (e.g. USD), however the second plot will look similarly, even if the points deviate slightly:

Another important difference is the one between monthly and yearly XRs, difference depicted by the below plot:

The value differences between the two XR types can have considerable impact on reporting. Therefore, one must reflect in analyses the rate type used in the actual process. 

Attempting to project data into the future can require complex techniques, however, sometimes is enough to highlight a probable area, which depends also on the confidence interval (e.g. 85%) and the forecast length (e.g. 10 months):

Every perspective into the data tends to provide something new that helps in sense-making. For some users the first table with flexible filtering (e.g. time unit, currency type, currency from/to) is enough, while for others multiple perspectives are needed. When possible, one should  allow users to explore the various perspectives and use the feedback to remove or even add more perspectives. Including a feedback loop in graphical representation is important not only for tailoring the visuals to users' needs but also for managing their expectations,  respectively of learning what works and what doesn't.

Comments:
1) I used GBP to NOK XRs to provide an example based on  triangulation.
2) Some experts advise against using borders or grid lines. Borders, as the name indicates allow to delimitate between various areas, while grid lines allow to make comparisons within a section without needing to sway between broader areas, adding thus precision to our senses-making. Choosing grey as color for the elements from the background minimizes the overhead for coping with more information while allowing to better use the available space.
3) Trend lines are recommended where the number of points is relatively small and only one series is involved, though, as always, there are exceptions too. 
4) In heatmaps one can use a gradient between two colors to show the tendencies of moving toward an extreme or another. One should avoid colors like red or green.
5) Ideally, a color should be used for only one encoding (e.g. one color for the same month across all graphics), though the more elements need to be encoded, the more difficult it becomes to respect this rule. The above graphics might slightly deviate from this as the purpose is to show a representation technique. 
6) In some graphics the XRs are displayed only with two decimals because currently the technique used (visual calculations) doesn't support formatting.
7) All the above graphical elements are based on a Power BI solution. Unfortunately, the tool has its representational limitations, especially when one wants to add additional information into the plots. 
8) Unfortunately, the daily XR values are not easily available from the same source. There are special scenarios for which a daily, hourly or even minute-based analysis is needed.
9) It's a good idea to validate the results against the similar results available on the web (see the ECB website).

Previous Post <<||>> Next Post

Project Management: The Butterflies of Project Management

Expressed metaphorically as "the flap of a butterfly’s wings in Brazil set off a tornado in Texas”, in Chaos Theory the “butterfly effect” is a hypothesis rooted in Edward N Lorenz’s work on weather forecasting and used to depict the sensitive dependence on initial conditions in nonlinear processes, systems in which the change in input is not proportional to the change in output.  

Even if overstated, the flapping of wings advances the idea that a small change (the flap of wings) in the initial conditions of a system cascades to a large-scale chain of events leading to large-scale phenomena (the tornado) . The chain of events is known as the domino effect and represents the cumulative effect produced when one event sets off a chain of similar events. If the butterfly metaphor doesn’t catch up maybe it’s easier to visualize the impact as a big surfing wave – it starts small and increases in size to the degree that it can bring a boat to the shore or make an armada drown under its force. 

Projects start as narrow activities however the longer they take and the broader they become tend to accumulate force and behave like a wave, having the force to push or drawn an organization in the flood that comes with it. A project is not only a system but a complex ecosystem - aggregations of living organisms and nonliving components with complex interactions forming a unified whole with emergent behavior deriving from the structure rather than its components - groups of people tend to  self-organize, to swarm in one direction or another, much like birds do, while knowledge seems to converge from unrelated sources (aka consilience). 

 Quite often ignored, the context in which a project starts is very important, especially because these initial factors or conditions can have a considerable impact reflected in people’s perception regarding the state or outcomes of the project, perception reflected eventually also in the decisions made during the later phases of the project. The positive or negative auspices can be easily reinforced by similar events. Given the complex correlations and implications, aspects not always correct perceived and understood can have a domino effect. 

The preparations for the project start – the Business Case, setting up the project structure, communicating project’s expectation and addressing stakeholders’ expectations, the kick-off meeting, the approval of the needed resources, the knowledge available in the team, all these have a certain influence on the project. A bad start can haunt a project long time after its start, even if the project is on the right track and makes a positive impact. In reverse, a good start can shade away some mishaps on the way, however there’s also the danger that the mishaps are ignored and have greater negative impact on the project. It may look as common sense however the first image often counts and is kept in people’s memory for a long time. 

As people are higher perceptive to negative as to positive events, there are higher the chances that a multitude of negative aspects will have bigger impact on the project. It’s again something that one can address as the project progresses. It’s not necessarily about control but about being receptive to the messages around and of allowing people to give (constructive) feedback early in the project. It’s about using the positive force of a wave and turning negative flow into a positive one. 

Being aware of the importance of the initial context is just a first step toward harnessing waves or winds’ power, it takes action and leadership to pull the project in the right direction.

Data Science: Forecasting (Just the Quotes)

"Extrapolations are useful, particularly in the form of soothsaying called forecasting trends. But in looking at the figures or the charts made from them, it is necessary to remember one thing constantly: The trend to now may be a fact, but the future trend represents no more than an educated guess. Implicit in it is 'everything else being equal' and 'present trends continuing'. And somehow everything else refuses to remain equal." (Darell Huff, "How to Lie with Statistics", 1954)

"When numbers in tabular form are taboo and words will not do the work well as is often the case. There is one answer left: Draw a picture. About the simplest kind of statistical picture or graph, is the line variety. It is very useful for showing trends, something practically everybody is interested in showing or knowing about or spotting or deploring or forecasting." (Darell Huff, "How to Lie with Statistics", 1954)

"The moment you forecast you know you’re going to be wrong, you just don’t know when and in which direction." (Edgar R Fiedler, 1977)

"Many of the basic functions performed by neural networks are mirrored by human abilities. These include making distinctions between items (classification), dividing similar things into groups (clustering), associating two or more things (associative memory), learning to predict outcomes based on examples (modeling), being able to predict into the future (time-series forecasting), and finally juggling multiple goals and coming up with a good- enough solution (constraint satisfaction)." (Joseph P Bigus,"Data Mining with Neural Networks: Solving business problems from application development to decision support", 1996)

"Probability theory is a serious instrument for forecasting, but the devil, as they say, is in the details - in the quality of information that forms the basis of probability estimates." (Peter L Bernstein, "Against the Gods: The Remarkable Story of Risk", 1996)

"Under conditions of uncertainty, both rationality and measurement are essential to decision-making. Rational people process information objectively: whatever errors they make in forecasting the future are random errors rather than the result of a stubborn bias toward either optimism or pessimism. They respond to new information on the basis of a clearly defined set of preferences. They know what they want, and they use the information in ways that support their preferences." (Peter L Bernstein, "Against the Gods: The Remarkable Story of Risk", 1996)

"Time-series forecasting is essentially a form of extrapolation in that it involves fitting a model to a set of data and then using that model outside the range of data to which it has been fitted. Extrapolation is rightly regarded with disfavour in other statistical areas, such as regression analysis. However, when forecasting the future of a time series, extrapolation is unavoidable." (Chris Chatfield, "Time-Series Forecasting" 2nd Ed, 2000)

"Models can be viewed and used at three levels. The first is a model that fits the data. A test of goodness-of-fit operates at this level. This level is the least useful but is frequently the one at which statisticians and researchers stop. For example, a test of a linear model is judged good when a quadratic term is not significant. A second level of usefulness is that the model predicts future observations. Such a model has been called a forecast model. This level is often required in screening studies or studies predicting outcomes such as growth rate. A third level is that a model reveals unexpected features of the situation being described, a structural model, [...] However, it does not explain the data." (Gerald van Belle, "Statistical Rules of Thumb", 2002)

"Most long-range forecasts of what is technically feasible in future time periods dramatically underestimate the power of future developments because they are based on what I call the 'intuitive linear' view of history rather than the 'historical exponential' view." (Ray Kurzweil, "The Singularity is Near", 2005)

"A forecaster should almost never ignore data, especially when she is studying rare events […]. Ignoring data is often a tip-off that the forecaster is overconfident, or is overfitting her model - that she is interested in showing off rather than trying to be accurate."  (Nate Silver, "The Signal and the Noise: Why So Many Predictions Fail-but Some Don't", 2012)

"Whether information comes in a quantitative or qualitative flavor is not as important as how you use it. [...] The key to making a good forecast […] is not in limiting yourself to quantitative information. Rather, it’s having a good process for weighing the information appropriately. […] collect as much information as possible, but then be as rigorous and disciplined as possible when analyzing it. [...] Many times, in fact, it is possible to translate qualitative information into quantitative information." (Nate Silver, "The Signal and the Noise: Why So Many Predictions Fail-but Some Don't", 2012)

"In common usage, prediction means to forecast a future event. In data science, prediction more generally means to estimate an unknown value. This value could be something in the future (in common usage, true prediction), but it could also be something in the present or in the past. Indeed, since data mining usually deals with historical data, models very often are built and tested using events from the past." (Foster Provost & Tom Fawcett, "Data Science for Business", 2013)

"Using random processes in our models allows economists to capture the variability of time series data, but it also poses challenges to model builders. As model builders, we must understand the uncertainty from two different perspectives. Consider first that of the econometrician, standing outside an economic model, who must assess its congruence with reality, inclusive of its random perturbations. An econometrician’s role is to choose among different parameters that together describe a family of possible models to best mimic measured real world time series and to test the implications of these models. I refer to this as outside uncertainty. Second, agents inside our model, be it consumers, entrepreneurs, or policy makers, must also confront uncertainty as they make decisions. I refer to this as inside uncertainty, as it pertains to the decision-makers within the model. What do these agents know? From what information can they learn? With how much confidence do they forecast the future? The modeler’s choice regarding insiders’ perspectives on an uncertain future can have significant consequences for each model’s equilibrium outcomes." (Lars P Hansen, "Uncertainty Outside and Inside Economic Models", [Nobel lecture] 2013)

"One important thing to bear in mind about the outputs of data science and analytics is that in the vast majority of cases they do not uncover hidden patterns or relationships as if by magic, and in the case of predictive analytics they do not tell us exactly what will happen in the future. Instead, they enable us to forecast what may come. In other words, once we have carried out some modelling there is still a lot of work to do to make sense out of the results obtained, taking into account the constraints and assumptions in the model, as well as considering what an acceptable level of reliability is in each scenario." (Jesús Rogel-Salazar, "Data Science and Analytics with Python", 2017)

"Regression describes the relationship between an exploratory variable (i.e., independent) and a response variable (i.e., dependent). Exploratory variables are also referred to as predictors and can have a frequency of more than 1. Regression is being used within the realm of predictions and forecasting. Regression determines the change in response variable when one exploratory variable is varied while the other independent variables are kept constant. This is done to understand the relationship that each of those exploratory variables exhibits." (Danish Haroon, "Python Machine Learning Case Studies", 2017)

"The first myth is that prediction is always based on time-series extrapolation into the future (also known as forecasting). This is not the case: predictive analytics can be applied to generate any type of unknown data, including past and present. In addition, prediction can be applied to non-temporal (time-based) use cases such as disease progression modeling, human relationship modeling, and sentiment analysis for medication adherence, etc. The second myth is that predictive analytics is a guarantor of what will happen in the future. This also is not the case: predictive analytics, due to the nature of the insights they create, are probabilistic and not deterministic. As a result, predictive analytics will not be able to ensure certainty of outcomes." (Prashant Natarajan et al, "Demystifying Big Data and Machine Learning for Healthcare", 2017)

"We know what forecasting is: you start in the present and try to look into the future and imagine what it will be like. Backcasting is the opposite: you state your desired vision of the future as if it’s already happened, and then work backward to imagine the practices, policies, programs, tools, training, and people who worked in concert in a hypothetical past (which takes place in the future) to get you there." (Eben Hewitt, "Technology Strategy Patterns: Architecture as strategy" 2nd Ed., 2019)

"Ideally, a decision maker or a forecaster will combine the outside view and the inside view - or, similarly, statistics plus personal experience. But it’s much better to start with the statistical view, the outside view, and then modify it in the light of personal experience than it is to go the other way around. If you start with the inside view you have no real frame of reference, no sense of scale - and can easily come up with a probability that is ten times too large, or ten times too small." (Tim Harford, "The Data Detective: Ten easy rules to make sense of statistics", 2020)

Data Science: Forecast/Forecasting (Definitions)

"1. A projection or an estimate of future sales, revenue, earnings, or costs. 2. A projection of future financial position and operating results of an organization." (Jae K Shim & Joel G Siegel, "Budgeting Basics and Beyond", 2008)

"The outcome of a series of exercises and analysis that helps a company, division, or product group to predict the number of units they might sell or produce, or the market share they could attain." (Steven Haines, "The Product Manager's Desk Reference", 2008)

"An estimate or prediction of conditions and events in the project's future, based on information and knowledge available at the time of the forecast. The information is based on the project's past performance and expected future performance, and includes information that could impact the project in the future, such as estimate at completion and estimate to complete." (Project Management Institute, "Practice Standard for Project Estimating", 2010)

"Refers to the operation responding to a wish to 'see in advance' what will happen later in a given field. Forecasting methods typically rely on data from the past to make forward-looking extrapolations; they assume continuity with possible inflections based on expert opinion(s)." (Humbert Lesca & Nicolas Lesca, "Weak Signals for Strategic Intelligence: Anticipation Tool for Managers", 2011)

"Anticipating the future using quantitative techniques, such as mathematical and statistical rules and analysis of past data to predict the future, plus qualitative techniques, such as expert judgment and opinions to validate or adjust predictions." (Joan C Dessinger, "Fundamentals of Performance Improvement" 3rd Ed., 2012)

"A numerical prediction of a future value for a time series. Forecasting techniques are used to identify previously unseen trends and anticipate fluctuations to facilitate better planning." (Jim Davis & Aiman Zeid, "Business Transformation: A Roadmap for Maximizing Organizational Insights", 2014)

"The practice of predicting or estimating a future event or trend, typically from historical data." (Brenda L Dietrich et al, "Analytics Across the Enterprise", 2014)

"A planning tool to help management to cope with the uncertainty of the future. It is based on certain assumptions based on management’s experience, knowledge and judgment and these estimates are projected into the future using techniques such as Box-Jenkins models, Delphi method, exponential smoothing, moving averages, regression analysis and trend projection. The technique of sensitivity analysis is also often used which assigns a range of values to uncertain variables in order to reduce potential errors." (Duncan Angwin & Stephen Cummings, "The Strategy Pathfinder" 3rd Ed., 2017)

"Estimates or predictions of conditions and events in the project's future based on information and knowledge available at the time of the forecast. Forecasts are updated and reissued based on work performance information provided as the project is executed." (Project Management Institute, "Practice Standard for Scheduling" 3rd Ed., 2019)

"Forecast usually refers to a projected value for a metric. Organizations will often create a forecast that is different than their target for a given metric. There are multiple types of forecasting methods for creating forecasts based on past data and usage of them varies widely across organizations." (Intrafocus)

Data Science: Delphi Method (Definitions)

 "A qualitative forecasting method that seeks to use the judgment of experts systematically in arriving at a forecast of what future events will be or when they may occur. It brings together a group of experts who have access to each other's opinions in an environment where no majority opinion is disclosed." (Jae K Shim & Joel G Siegel, "Budgeting Basics and Beyond", 2008)

"A systematic forecasting practice that seeks input or advice from a panel of experts. Each expert provides their forecast input in a successive series of rounds, until consensus is achieved." (Steven Haines, "The Product Manager's Desk Reference", 2008)

"A systematic, interactive forecasting method that relies on a panel of experts. The experts answer questionnaires in two or more rounds. After each round, a facilitator provides an anonymous summary of the experts’ forecasts from the previous round as well as the reasons they provided for their judgments." (Project Management Institute, "Practice Standard for Project Estimating", 2010)

"Data collection method that happens in an anonymous fashion." (Adam Gordon, "Official (ISC)2 Guide to the CISSP CBK" 4th Ed., 2015)

"A structured communication technique used to conduct interactive forecasting. It involves a panel of experts." (IQBBA)

Systems Engineering: Complex Systems (Definitions)

"Roughly, by a complex system I mean one made up of a large number of parts that interact in a nonsimple way." (Herbert Simon, "The Architecture of Complexity", Proceedings of the American Philosophical Society Vol. 106 (6), 1962)

"A complex system is one which possesses mathematical images which are not dynamical systems." (Robert Rosen, On complex systems, European Journal of Operational Research Vol. 30 (2), 1987)

"A complex system is a system formed out of many components whose behavior is emergent, that is, the behavior of the system cannot be simply inferred from the behavior of its components." (Yaneer Bar-Yamm, "Dynamics of Complexity", 1997)

"A system may be called complex here if its dimension (order) is too high and its model (if available) is nonlinear, interconnected, and information on the system is uncertain such that classical techniques can not easily handle the problem." (M Jamshidi, Autonomous Control on Complex Systems: Robotic Applications, Current Advances in Mechanical Design and Production VII, 2000)

"A highly coupled system where the outcomes of the system are the result of the interactions that occur between its different components." (David Lyell et al, "Health Systems Simulation", Encyclopedia of Healthcare Information Systems, 2008)

"Network-based systems characterized by feedback-driven flow of information, openness, self-organization, and emergence. (Ani Calinescu & Janet Efstathiou, "Measures of Network Structure", Encyclopedia of Networked and Virtual Organizations, 2008) 

"[a complex system is] a system in which large networks of components with no central control and simple rules of operation give rise to complex collective behavior, sophisticated information processing, and adaptation via learning or evolution." (Melanie Mitchell, "Complexity: A Guided Tour", 2009)

"Systems made of several interconnected simple parts which altogether exhibit a high degree of complexity from each emerges a higher order behaviour." (Radu Mutihac, "Mathematical Modeling of Artificial Neural Networks", Encyclopedia of Artificial Intelligence, 2009)

"CS [complex system] is a system composed of many heterogeneous agents, which are nonlinearly interconnected, while the final emergence of the system is completely different than the individual element`s performance." (Shahrooz V Manesha & Massimo Tadi, "Sustainable urban morphology emergence via complex adaptive system analysis: sustainable design in existing contex", Procedia Engineering 21, 2011)

"A system that exhibits a mutual interdependency of components and for which a change in the input parameter(s) can result in a non-proportional large or small change of the system output." (Alexander Kolker, Management Science for Healthcare Applications, Encyclopedia of Business Analytics and Optimization, 2014) 

"A system whose intricacy impedes the forecasting of its behaviour." (Valentina M Ghinea, "Modelling and Simulation of the Need for Harmonizing the European Higher Education Systems", Handbook of Research on Trends in European Higher Education Convergence, 2014)

"A system which is usually composed of large number of possibly heterogeneous interacting agents, which are seen to exhibit emergent behavior." (Stephen E Glavin & Abhijit Sengupta, "Modelling of Consumer Goods Markets: An Agent-Based Computational Approach", Handbook of Research on Managing and Influencing Consumer Behavior, 2015)

"Complex systems are networks made of a number of components that interact with each other, typically in a nonlinear fashion. Complex systems may arise and evolve through self-organization, such that they are neither completely regular nor completely random, permitting the development of emergent behavior at macroscopic scales." (Hiroki Sayama, "Introduction to the Modeling and Analysis of Complex Systems", 2015)

"The occurrence of new phenomena generated unpredictably by the interaction of simple rules and individual mechanisms that are in constant flux and interaction. Emergence suggests something novel is perpetually emerging at a systems/global level as the world and environment constantly shifts and changes at a mechanistic/local level." (Kathy Sanford & Tim Hopper, "Digital Media in the Classroom: Emergent Perspectives for 21st Century Learners", Handbook of Research on Digital Media and Creative Technologies, 2015)

"A system characterized by the number of the elements that constitute it, and by the nature of the interactions between these elements." (Manuela Piscitelli, "Application of Complexity Theory in Representation of the City", Handbook of Research on Chaos and Complexity Theory in the Social Sciences, 2016)

"A complex system means a system whose perceived complicated behaviors can be attributed to one or more of the following characteristics: large number of element, large number of relationships among elements, non-linear and discontinuous relationship, and uncertain characteristics of elements." (Chunfang Zhou, "Fostering Creative Problem Solvers in Higher Education: A Response to Complexity of Societies", Handbook of Research on Creative Problem-Solving Skill Development in Higher Education, 2017)

"System made up of many interconnected elements on various levels; interactions on lower levels give rise to events on higher levels." (Naomi Thompson & Joshua Danish, "Designing BioSim: Playfully Encouraging Systems Thinking in Young Children", Handbook of Research on Serious Games for Educational Applications, 2017)

Galit Shmueli - Collected Quotes

"Extreme values are values that are unusually large or small compared to other values in the series. Extreme va- lue can affect different forecasting methods to various degrees. The decision whether to remove an extreme value or not must rely on information beyond the data. Is the extreme value the result of a data entry error? Was it due to an unusual event (such as an earthquake) that is unlikely to occur again in the forecast horizon? If there is no grounded justification to remove or replace the extreme value, then the best practice is to generate two sets of forecasts: those based on the series with the extreme values and those based on the series excluding the extreme values." (Galit Shmueli, "Practical Time Series Forecasting: A Hands-On Guide", 2011)

"For the purpose of choosing adequate forecasting methods, it is useful to dissect a time series into a systematic part and a non-systematic part. The systematic part is typically divided into three components: level , trend , and seasonality. The non-systematic part is called noise. The systematic components are assumed to be unobservable, as they characterize the underlying series, which we only observe with added noise." (Galit Shmueli, "Practical Time Series Forecasting: A Hands-On Guide", 2011)

"Forecasting methods attempt to isolate the systematic part and quantify the noise level. The systematic part is used for generating point forecasts and the level of noise helps assess the uncertainty associated with the point forecasts." (Galit Shmueli, "Practical Time Series Forecasting: A Hands-On Guide", 2011)

"Missing values in a time series create "holes" in the series. The presence of missing values has different implications and requires different action depending on the forecasting method." (Galit Shmueli, "Practical Time Series Forecasting: A Hands-On Guide", 2011)

"[…] noise is the random variation that results from measurement error or other causes not accounted for. It is always present in a time series to some degree, although we cannot observe it directly." (Galit Shmueli, "Practical Time Series Forecasting: A Hands-On Guide", 2011)

"Some forecasting methods directly model these components by making assumptions about their structure. For example, a popular assumption about trend is that it is linear or exponential over parts, or all, of the given time period. Another common assumption is about the noise structure: many statistical methods assume that the noise follows a normal distribution. The advantage of methods that rely on such assumptions is that when the assumptions are reasonably met, the resulting forecasts will be more robust and the models more understandable." (Galit Shmueli, "Practical Time Series Forecasting: A Hands-On Guide", 2011)

"Overfitting means that the model is not only fitting the systematic component of the data, but also the noise. An over-fitted model is therefore likely to perform poorly on new data." (Galit Shmueli, "Practical Time Series Forecasting: A Hands-On Guide", 2011)

"Understanding how performance is evaluated affects the choice of forecasting method, as well as the particular details of how a particular forecasting method is executed." (Galit Shmueli, "Practical Time Series Forecasting: A Hands-On Guide", 2011)

"When the purpose of forecasting is to generate accurate forecasts, it is useful to define performance metrics that measure predictive accuracy. Such metrics can tell us how well a particular method performs in general, as well as compared to benchmarks or forecasts from other methods." (Galit Shmueli, "Practical Time Series Forecasting: A Hands-On Guide", 2011)