What Is an Autoregressive Integrated Moving Average (ARIMA)?

An autoregressive integrated moving average, or ARIMA, is a statistical analysis model that uses time series data to either better understand the data set or to predict future trends. 

A statistical model is autoregressive if it predicts future values based on past values. For example, an ARIMA model might seek to predict a stock’s future prices based on its past performance or forecast a company’s earnings based on past periods.

Understanding Autoregressive Integrated Moving Average (ARIMA)

An autoregressive integrated moving average model is a form of regression analysis that gauges the strength of one dependent variable relative to other changing variables. The model’s goal is to predict future securities or financial market moves by examining the differences between values in the series instead of through actual values.

An ARIMA model can be understood by outlining each of its components as follows:

• Autoregression (AR): refers to a model that shows a changing variable that regresses on its own lagged, or prior, values.
• Integrated (I): represents the differencing of raw observations to allow the time series to become stationary (i.e., data values are replaced by the difference between the data values and the previous values).
• Moving average (MA):  incorporates the dependency between an observation and a residual error from a moving average model applied to lagged observations.

ARIMA Parameters

Each component in ARIMA functions as a parameter with a standard notation. For ARIMA models, a standard notation would be ARIMA with p, d, and q, where integer values substitute for the parameters to indicate the type of ARIMA model used. The parameters can be defined as:

• p: the number of lag observations in the model, also known as the lag order.
• d: the number of times the raw observations are differenced; also known as the degree of differencing.
• q: the size of the moving average window, also known as the order of the moving average.

For example, a linear regression model includes the number and type of terms. A value of zero (0), which can be used as a parameter, would mean that particular component should not be used in the model. This way, the ARIMA model can be constructed to perform the function of an ARMA model, or even simple AR, I, or MA models.

ARIMA and Stationary Data

In an autoregressive integrated moving average model, the data are differenced in order to make it stationary. A model that shows stationarity is one that shows there is constancy to the data over time. Most economic and market data show trends, so the purpose of differencing is to remove any trends or seasonal structures. 

Seasonality, or when data show regular and predictable patterns that repeat over a calendar year, could negatively affect the regression model. If a trend appears and stationarity is not evident, many of the computations throughout the process cannot be made and produce the intended results.

How to Build an ARIMA Model

To begin building an ARIMA model for an investment, you download as much of the price data as you can. Once you’ve identified the trends for the data, you identify the lowest order of differencing (d) by observing the autocorrelations. If the lag-1 autocorrelation is zero or negative, the series is already differenced. You may need to difference the series more if the lag-1 is higher than zero.

Next, determine the order of regression (p) and order of moving average (q) by comparing autocorrelations and partial autocorrelations. Once you have the information you need, you can choose the model you’ll use.

Pros and Cons of ARIMA

ARIMA models have strong points and are good at forecasting based on past circumstances, but there are more reasons to be cautious when using ARIMA. In stark contrast to investing disclaimers that state “past performance is not an indicator of future performance…,” ARIMA models assume that past values have some residual effect on current or future values and use data from the past to forecast future events.

The following table lists other ARIMA traits that demonstrate good and bad characteristics.

The Bottom Line

The ARIMA model is used as a forecasting tool to predict how something will act in the future based on past performance. It is used in technical analysis to predict an asset’s future performance.

ARIMA modeling is generally inadequate for long-term forecastings, such as more than six months ahead, because it uses past data and parameters that are influenced by human thinking. For this reason, it is best used with other technical analysis tools to get a clearer picture of an asset’s performance.

What Is Average Propensity to Consume?

Average propensity to consume (APC) measures the percentage of income that is spent rather than saved. This may be calculated by a single individual who wants to know where the money is going or by an economist who wants to track the spending and saving habits of an entire nation.

In either case, the propensity to consume can be determined by dividing average household consumption, or spending, by average household income, or earnings.

Understanding Average Propensity to Consume

From the broader economic view, a high average propensity to consume is generally good for the economy. When the average propensity to consume is high, consumers are saving less and spending more on goods or services. This increased demand drives economic growth, business expansion, and broad employment.

Low-income households are often seen as having a higher average propensity to consume than high-income households. Low-income households may be forced to spend their entire income on necessities with minimal disposable income remaining to save. Alternatively, high-income households with higher cash flow after their necessities are met typically have a relatively lower average propensity to consume.

Economists often gauge economy forecasts on actions by the middle-income households. The spending and savings patterns of this demographic often indicate a degree of confidence or pessimism about their own personal financial situations and the economy as a whole.

Propensity to Consume vs. Propensity to Save

The sum of the average propensity to consume and the average propensity to save is always equivalent to one. A household or a nation must either spend or save all of its income.

The inverse of the average propensity to consume is the average propensity to save (APS). That figure is simply the total of income minus spending. The result is known as the savings ratio.

Notably, the savings ratio is normally based on its percentage of disposable income, or after-tax income. An individual determining personal propensities to consume and save should probably use the disposable income figure as well for a more realistic measure.

Example of Average Propensity to Consume

Assume a nation’s economy has a gross domestic product (GDP) equivalent to its disposable income of $500 billion for the previous year. The total savings of the economy was $300 billion, and the rest was spent on goods and services.

The nation’s APS is calculated to be 0.60, or $300 billion/$500 billion. This indicates the economy allocated 60% of its disposable income to savings. The average propensity to consume is calculated to be 0.40, or (1 – 0.60). Therefore, the nation spent 40% of its GDP on goods and services.

APS can include saving for retirement, a home purchase, and other long-term investments. As such, it can be a proxy for national financial health.

Special Considerations

The marginal propensity to consume (MPC) is a related concept. It measures the change in the average propensity to consume.

Assume that the nation in the previous example increased its GDP to $700 billion and its consumption of goods and services rose to $375 billion. The economy’s average propensity to consume increased to 53.57%.

The nation’s consumption increased from $200 billion to $375 billion. Alternatively, the nation’s GDP increased from $500 billion to $700 billion. The nation’s marginal propensity to consume is 87.5% ($375 billion – $200 billion) / ($700 billion – $500 billion). The marginal propensity measures the directional trend of how an entity is utilizing its money. In this case, 87.5% of new growth was further consumed.

What Is the Average Age of Inventory?

The average age of inventory is the average number of days it takes for a firm to sell off inventory. It is a metric that analysts use to determine the efficiency of sales. The average age of inventory is also referred to as days’ sales in inventory (DSI).

Formula and Calculation of Average Age of Inventory

The formula to calculate the average age of inventory is:


$\begin{aligned} &\text{Average Age of Inventory}= \frac{ C }{ G } \times 365 \\ &\textbf{where:} \\ &C = \text{The average cost of inventory at its present level} \\ &G = \text{The cost of goods sold (COGS)} \\ \end{aligned}$​Average Age of Inventory=GC​×365where:C=The average cost of inventory at its present levelG=The cost of goods sold (COGS)​

What the Average Age of Inventory Can Tell You

The average age of inventory tells the analyst how fast inventory is turning over at one company compared to another. The faster a company can sell inventory for a profit, the more profitable it is. However, a company could employ a strategy of maintaining higher levels of inventory for discounts or long-term planning efforts. While the metric can be used as a measure of efficiency, it should be confirmed with other measures of efficiency, such as gross profit margin, before making any conclusions.

The average age of inventory is a critical figure in industries with rapid sales and product cycles, such as the technology industry. A high average age of inventory can indicate that a firm is not properly managing its inventory or that it has an inventory that is difficult to sell.

The average age of inventory helps purchasing agents make buying decisions and managers make pricing decisions, such as discounting existing inventory to move products and increase cash flow. As a firm’s average age of inventory increases, its exposure to obsolescence risk also grows. Obsolescence risk is the risk that the value of inventory loses its value over time or in a soft market. If a firm is unable to move inventory, it can take an inventory write-off for some amount less than the stated value on a firm’s balance sheet.

Example of How to Use the Average Age of Inventory

An investor decides to compare two retail companies. Company A owns inventory valued at $100,000 and the COGS is $600,000. The average age of Company A’s inventory is calculated by dividing the average cost of inventory by the COGS and then multiplying the product by 365 days. The calculation is $100,000 divided by $600,000, multiplied by 365 days. The average age of inventory for Company A is 60.8 days. That means it takes the firm approximately two months to sell its inventory.

Conversely, Company B also owns inventory valued at $100,000, but the cost of inventory sold is $1 million, which reduces the average age of inventory to 36.5 days. On the surface, Company B is more efficient than Company A.

What Is Average Outstanding Balance?

An average outstanding balance is the unpaid, interest-bearing balance of a loan or loan portfolio averaged over a period of time, usually one month. The average outstanding balance can refer to any term, installment, revolving, or credit card debt on which interest is charged. It may also be an average measure of a borrower’s total outstanding balances over a period of time.

Average outstanding balance can be contrasted with average collected balance, which is that part of the loan that has been repaid over the same period.

Understanding Average Outstanding Balance

Average outstanding balances can be important for several reasons. Lenders often have a portfolio of many loans, which need to be assessed in aggregate in terms of risk and profitability. Banks use the average outstanding balance to determine the amount of interest they pay each month to their account holders or charge to their borrowers. If a bank has a large outstanding balance on its lending portfolio it could indicate that they are having trouble collecting on their loans and may be a signal for future financial stress.

Many credit card companies also use an average daily outstanding balance method for calculating interest applied to a revolving credit loan, particularly credit cards. Credit card users accumulate outstanding balances as they make purchases throughout the month. An average daily balance method allows a credit card company to charge slightly higher interest that takes into consideration a cardholder’s balances throughout the past days in a period and not just at the closing date.

For borrowers, credit rating agencies will review a consumer’s outstanding balances on their credit cards as part of determining a FICO credit score. Borrowers should show restraint by keeping their credit card balances well below their limits. Maxing out credit cards, paying late, and applying for new credit increases one’s outstanding balances and can lower FICO scores.

Interest on Average Outstanding Balances 

With average daily outstanding balance calculations, the creditor may take an average of the balances over the past 30 days and assess interest on a daily basis. Commonly, average daily balance interest is a product of the average daily balances over a statement cycle with interest assessed on a cumulative daily basis at the end of the period.

Regardless, the daily periodic rate is the annual percentage rate (APR) divided by 365. If interest is assessed cumulatively at the end of a cycle, it would only be assessed based on the number of days in that cycle.

Other average methodologies also exist. For example, a simple average may be used between a beginning and ending date by dividing the beginning balance plus the ending balance by two and then assessing interest based on a monthly rate.

Credit cards will provide their interest methodology in the cardholder agreement. Some companies may provide details on interest calculations and average balances in their monthly statements.

Consumer Credit

Outstanding balances are reported by credit providers to credit reporting agencies each month. Credit issuers typically report a borrower’s total outstanding balance at the time the report is provided. Some credit issuers may report outstanding balances at the time a statement is issued while others choose to report data on a specific day each month. Balances are reported on all types of revolving and non-revolving debt. With outstanding balances, credit issuers also report delinquent payments beginning at 60 days past due.

Timeliness of payments and outstanding balances are the top factors that affect a borrower’s credit score. Experts say borrowers should strive to keep their total outstanding balances below 30%. Borrowers using more than 30% of total available debt outstanding can easily improve their credit score from month to month by making larger payments that reduce their total outstanding balance.

When the total outstanding balance decreases, a borrower’s credit score improves. Timeliness, however, is not as easy to improve since delinquent payments are a factor that can remain on a credit report for seven years.

Calculating Average Outstanding Balance

Lenders typically calculate interest on revolving credit, such as credit cardsor lines of credit, using an average of daily outstanding balances. The bank adds all the daily outstanding balances in the period (usually a month) and divides this sum by the number of days in the period. The result is the average outstanding balance for the period.

For loans that are paid monthly, such as mortgages, a lender may instead take the arithmetic mean of the starting and ending balance for a statement cycle. For instance, say a home borrower has a mortgage balance of $100,000 at the start of the month and makes a payment on the 30th of the same month, reducing the outstanding principal amount to $99,000. The average outstanding balance for the loan over that period would be ($100,000-99,000)/2 = $99,500.

Frequently Asked Questions

What is an outstanding balance?

An outstanding balance is the total amount still owed on a loan.

What is an outstanding principal balance?

This is the amount of a loan’s principal amount (i.e. the dollar amount initially loaned) that is still due, and does not take into account the interest or any fees that are owed on the loan.

Where can I find my outstanding balance?

Borrowers can find this information on their regular bank or loan statements. They can also usually be pulled up from a lender’s website for viewing at any time.

What is the difference between outstanding balance and remaining balance?

Outstanding balance refers to the amount still owed on a loan from the perspective of a borrower or lender. Remaining balance instead refers to how much money remains in an account after spending or a withdrawal, from the perspective of a saver or savings bank.

What percentage of an outstanding balance is a minimum payment?

Some lenders charge a fixed percentage, such a 2.5%. Others will charge a flat fee plus a fixed percentage, such as $20 + 1.75% of the outstanding balance as the minimum payment due. Penalty fees like late fees, as well as past due amounts, will typically be added to the calculation. This would increase your minimum payment significantly.