Stock Price Trends
Stock price trends estimated using linear regression.
Summary
Key facts
- The primary trend is decreasing.
- The decline rate of the primary trend is 12.87% per annum.
- NKE price at the close of April 26, 2024 was $94.12 and was inside the primary price channel.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 44.59% per annum.
- NKE price at the close of April 26, 2024 was inside the secondary price channel.
Linear Regression Model
Model equation:
Yi = α + β × Xi + εi
Top border of price channel:
Exp(Yi) = Exp(a + b × Xi + 2 × s)
Bottom border of price channel:
Exp(Yi) = Exp(a + b × Xi – 2 × s)
where:
i - observation number
Yi - natural logarithm of NKE price
Xi - time index, 1 day interval
σ - standard deviation of εi
a - estimator of α
b - estimator of β
s - estimator of σ
Exp() - calculates the exponent of e
Primary Trend
Start date: December 3, 2020
End date: April 26, 2024
a = 5.2613
b = -0.0004
s = 0.1184
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0004) – 1
= -12.87%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.1184) – 1
= 60.56%
December 3, 2020 calculations
Top border of price channel:
Exp(Y405)
= Exp(a + b × X405 + 2 × s)
= Exp(a + b × 584 + 2 × s)
= Exp(5.2613 + -0.0004 × 584 + 2 × 0.1184)
= Exp(5.2777)
= $195.91
Bottom border of price channel:
Exp(Y405)
= Exp(a + b × X405 – 2 × s)
= Exp(a + b × 584 – 2 × s)
= Exp(5.2613 + -0.0004 × 584 – 2 × 0.1184)
= Exp(4.8042)
= $122.02
April 26, 2024 calculations
Top border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 + 2 × s)
= Exp(a + b × 1,824 + 2 × s)
= Exp(5.2613 + -0.0004 × 1,824 + 2 × 0.1184)
= Exp(4.8097)
= $122.70
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,824 – 2 × s)
= Exp(5.2613 + -0.0004 × 1,824 – 2 × 0.1184)
= Exp(4.3363)
= $76.42
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 12.87% per annum.
- NKE price at the close of April 26, 2024 was $94.12 and was inside the primary price channel.
Secondary Trend
Start date: December 1, 2023
End date: April 26, 2024
a = 7.4629
b = -0.0016
s = 0.0394
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0016) – 1
= -44.59%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0394) – 1
= 17.05%
December 1, 2023 calculations
Top border of price channel:
Exp(Y1,158)
= Exp(a + b × X1,158 + 2 × s)
= Exp(a + b × 1,677 + 2 × s)
= Exp(7.4629 + -0.0016 × 1,677 + 2 × 0.0394)
= Exp(4.8288)
= $125.06
Bottom border of price channel:
Exp(Y1,158)
= Exp(a + b × X1,158 – 2 × s)
= Exp(a + b × 1,677 – 2 × s)
= Exp(7.4629 + -0.0016 × 1,677 – 2 × 0.0394)
= Exp(4.6714)
= $106.85
April 26, 2024 calculations
Top border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 + 2 × s)
= Exp(a + b × 1,824 + 2 × s)
= Exp(7.4629 + -0.0016 × 1,824 + 2 × 0.0394)
= Exp(4.5910)
= $98.60
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,824 – 2 × s)
= Exp(7.4629 + -0.0016 × 1,824 – 2 × 0.0394)
= Exp(4.4336)
= $84.23
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 44.59% per annum.
- NKE price at the close of April 26, 2024 was inside the secondary price channel.
- Discover a new approach to trend analysis.
- Check the power of mathematical statistics.
- Price channels have never been so accurately estimated.
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