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<ManualTopic ID="/baanerp/cp/onlinemanual/000111" xml:lang="en">
	<Header>
		<Title xmlns:ssa="http://www.ssaglobal.com" xmlns:HTML="http://www.w3.org/TR/REC-html40">Forecast method: polynomial regression</Title>
		<Keyword><Level1>Forecast method: polynomial regression</Level1>
		</Keyword>
		<Keyword><Level1>Polynomial regression</Level1>
		</Keyword>
	</Header>
	<GeneralSection><Paragraph>SSA ERP calculates the demand forecast according to the <GUIRef href="/baanerp/cp/domains/rpd.fcmd#pr" role="enum">Polynomial Regression</GUIRef> forecast method on the basis of an n'th degree polynom, which matches the historic demand data.</Paragraph>
		<List><ListIntro>The relevant parameters for this forecast method are:</ListIntro>
			<ListItem><GUIRef href="/baanerp/cp/dsp/cpdsp1110m000#cpdsp110.dgpr" role="formfield">Degree for Polynomial Regression</GUIRef>
			</ListItem>
			<ListItem><GUIRef href="/baanerp/cp/dsp/cpdsp1110m000#cpdsp110.tosi" role="formfield">Type of Seasonal Influence</GUIRef>
			</ListItem>
			<ListItem><GUIRef href="/baanerp/cp/dsp/cpdsp1110m000#cpdsp110.sctm" role="formfield">Seasonal Cycle Time</GUIRef>
			</ListItem>
			<ListItem><GUIRef href="/baanerp/cp/dsp/cpdsp1110m000#cpdsp110.aufp" role="formfield">Automatic Update of Forecast Parameters</GUIRef>
			</ListItem>
		</List>
		<Paragraph>You can maintain these parameters in the <GUIRef href="/baanerp/cp/dsp/cpdsp1110m000" role="session">Plan Items - Forecast Settings (cpdsp1110m000)</GUIRef> session.</Paragraph>
		<Paragraph>The polynom's degree is indicated by the <GUIRef href="/baanerp/cp/dsp/cpdsp1110m000#cpdsp110.dgpr" role="formfield">Degree for Polynomial Regression</GUIRef> field. If the <GUIRef href="/baanerp/cp/dsp/cpdsp1110m000#cpdsp110.aufp" role="formfield">Automatic Update of Forecast Parameters</GUIRef> check box is selected, SSA ERP determines the polynom's optimum degree.</Paragraph>
		<GeneralSection><SectionTitle>Trend-adjusted average demand</SectionTitle>
			<Paragraph>First, the historical demand figures are adjusted with the trend-adjusted average demand for the relevant period.</Paragraph>
			<Paragraph>Without seasonal influence:</Paragraph>
			<Formula><Paragraph UserLevel="Novice" UserType="Taskuser">TD(t) =	 AV</Paragraph>
			</Formula>
			<Paragraph>With a linear trend influence:</Paragraph>
			<Formula><Paragraph UserLevel="Novice" UserType="Taskuser">TD(t) = CS + TF * t</Paragraph>
			</Formula>
			<Paragraph>With a progressive trend influence:</Paragraph>
			<Formula><Paragraph UserLevel="Novice" UserType="Taskuser">TD(t) = BS * TF ^ (t-1)DM(t) = AD(t) - TD(t)</Paragraph>
			</Formula>
			<Paragraph>Where:</Paragraph>
			<TABLE border="1"><TBODY><TR><TD>DM(t)</TD>
						<TD>trend-adjusted average demand for period t</TD>
					</TR>
					<TR><TD>TD(t)</TD>
						<TD>trend-based demand for period t</TD>
					</TR>
					<TR><TD>AD(t)</TD>
						<TD>actual demand for period t</TD>
					</TR>
					<TR><TD>AV</TD>
						<TD>average demand (*)</TD>
					</TR>
					<TR><TD>CS</TD>
						<TD>constant demand</TD>
					</TR>
					<TR><TD>BS</TD>
						<TD>estimated demand for period 1</TD>
					</TR>
					<TR><TD>TF</TD>
						<TD>trend factor</TD>
					</TR>
				</TBODY>
			</TABLE>
			<Paragraph>(*) The average demand is the sum of the historical demand figures by period, divided by the number of periods with demand history.</Paragraph>
		</GeneralSection>
		<GeneralSection><SectionTitle>Coefficients of the polynom</SectionTitle>
			<Paragraph>SSA ERP calculates the coefficients of the polynom with the polynomial regression method. See the Related topics for more information about polynomial regression.</Paragraph>
		</GeneralSection>
		<GeneralSection><SectionTitle>Demand forecast</SectionTitle>
			<Paragraph>SSA ERP calculates the demand for each forecast period based on the trend-adjusted average demand for the period in question, increased with the average noise in the past.</Paragraph>
		</GeneralSection>
		<GeneralSection><SectionTitle>Noise</SectionTitle>
			<Paragraph>The noise is the fluctuation of the demand data compared to the trend that has been determined. The average noise is determined for each forecast period based on the history periods which are a whole number of seasonal cycles ago.</Paragraph>
		</GeneralSection>
		<Note><SectionTitle>Note</SectionTitle>
			<Paragraph>If the <GUIRef href="/baanerp/cp/dsp/cpdsp1110m000#cpdsp110.tosi" role="formfield">Type of Seasonal Influence</GUIRef> field is <GUIRef href="/baanerp/cp/domains/rpd.tosi#not.in.use" role="enum">Not Applicable</GUIRef>, SSA ERP assumes a fictitious seasonal cycle with a season length of up to a quarter of the number of periods with historical demand.</Paragraph>
		</Note>
		<ExampleSection><SectionTitle>Example</SectionTitle>
			<Paragraph>Figure 1 shows the history demand data of two seasonal cycles, which consist of 8 forecast periods. Period 9 is the current period.</Paragraph>
			<Figure><HTML:IMG SRC="../images/nt_graph_000111a.gif" height="252" width="432" xmlns:ssa="http://www.ssaglobal.com" xmlns:HTML="http://www.w3.org/TR/REC-html40"/><FigCaption>Figure 1</FigCaption>
				<FigLegend><LegendEntry><Symbol>SCT</Symbol>
						<Desc>seasonal cycle time</Desc>
					</LegendEntry>
				</FigLegend>
			</Figure>
			<Paragraph>Figure 2 shows the polynom that is determined with polynomial regression.</Paragraph>
			<Figure><HTML:IMG SRC="../images/nt_graph_000111b.gif" height="252" width="432" xmlns:ssa="http://www.ssaglobal.com" xmlns:HTML="http://www.w3.org/TR/REC-html40"/><FigCaption>Figure 2</FigCaption>
			</Figure>
			<Paragraph>For each history period, the demand based on the polynom is compared to the trend of the demand. A linear trend is assumed to be present, characterized by the following formula:</Paragraph>
			<Formula><Paragraph UserLevel="Novice" UserType="Taskuser">TD(t) = CS + TF * t</Paragraph>
				<FigLegend><LegendEntry><Symbol>TD (t)</Symbol>
						<Desc>trend based demand for period t</Desc>
					</LegendEntry>
					<LegendEntry><Symbol>CS</Symbol>
						<Desc>constant demand (= 54)</Desc>
					</LegendEntry>
					<LegendEntry><Symbol>TF</Symbol>
						<Desc>trend factor (= 2)</Desc>
					</LegendEntry>
				</FigLegend>
			</Formula>
			<TABLE border="1"><TBODY><TR><TD>Period</TD>
						<TD>Polynom</TD>
						<TD>Trend</TD>
						<TD>Noise</TD>
					</TR>
					<TR><TD>1</TD>
						<TD>45</TD>
						<TD>56</TD>
						<TD>-11</TD>
					</TR>
					<TR><TD>2</TD>
						<TD>53</TD>
						<TD>58</TD>
						<TD>-5</TD>
					</TR>
					<TR><TD>3</TD>
						<TD>76</TD>
						<TD>60</TD>
						<TD>+16</TD>
					</TR>
					<TR><TD>4</TD>
						<TD>70</TD>
						<TD>62</TD>
						<TD>+8</TD>
					</TR>
					<TR><TD>5</TD>
						<TD>49</TD>
						<TD>64</TD>
						<TD>-15</TD>
					</TR>
					<TR><TD>6</TD>
						<TD>55</TD>
						<TD>66</TD>
						<TD>-11</TD>
					</TR>
					<TR><TD>7</TD>
						<TD>78</TD>
						<TD>68</TD>
						<TD>+10</TD>
					</TR>
					<TR><TD>8</TD>
						<TD>70</TD>
						<TD>70</TD>
						<TD>+0</TD>
					</TR>
				</TBODY>
			</TABLE>
			<Paragraph>The average noise based on these differences is added to the trend-adjusted demand. For example, the average noise for forecast period 9 is the average of the noise of periods 1 and 5.</Paragraph>
			<TABLE border="1"><TBODY><TR><TD>Forecast period</TD>
						<TD>Trend</TD>
						<TD>Average noise</TD>
						<TD>Based on periods</TD>
						<TD>Forecast demand</TD>
					</TR>
					<TR><TD>9</TD>
						<TD>72</TD>
						<TD>-13</TD>
						<TD>1,5</TD>
						<TD>59</TD>
					</TR>
					<TR><TD>10</TD>
						<TD>74</TD>
						<TD>-8</TD>
						<TD>2,6</TD>
						<TD>66</TD>
					</TR>
					<TR><TD>11</TD>
						<TD>76</TD>
						<TD>+13</TD>
						<TD>3,7</TD>
						<TD>89</TD>
					</TR>
					<TR><TD>12</TD>
						<TD>78</TD>
						<TD>+4</TD>
						<TD>4,8</TD>
						<TD>82</TD>
					</TR>
					<TR><TD>13</TD>
						<TD>80</TD>
						<TD>-13</TD>
						<TD>1,4</TD>
						<TD>67</TD>
					</TR>
					<TR><TD>14</TD>
						<TD>82</TD>
						<TD>-7</TD>
						<TD>2,6</TD>
						<TD>75</TD>
					</TR>
				</TBODY>
			</TABLE>
			<Paragraph>The result is shown in Figure 3.</Paragraph>
			<Figure><HTML:IMG SRC="../images/nt_graph_000111c.gif" height="252" width="432" xmlns:ssa="http://www.ssaglobal.com" xmlns:HTML="http://www.w3.org/TR/REC-html40"/><FigCaption>Figure 3</FigCaption>
			</Figure>
		</ExampleSection>
	</GeneralSection>
	<RelatedTopics><SectionTitle>Related topics</SectionTitle>
		<RelTopic><Link href="/baanerp/cp/onlinemanual/000079" role="manual">Algorithm for demand forecasting</Link>
		</RelTopic>
		<RelTopic><Link href="/baanerp/cp/onlinemanual/000321" role="manual">Forecasting methods</Link>
		</RelTopic>
		<RelTopic><Link href="/baanerp/cp/onlinemanual/000108" role="manual">Principle of polynomial regression</Link>
		</RelTopic>
	</RelatedTopics>
</ManualTopic>
