Stock Price Trends
Stock price trends estimated using linear regression.
Summary
Key facts
- The primary trend is increasing.
- The growth rate of the primary trend is 12.07% per annum.
- AAPL price at the close of April 29, 2024 was $173.50 and was inside the primary price channel.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 34.59% per annum.
- AAPL price at the close of April 29, 2024 was inside the secondary price channel.
- The direction of the secondary trend is opposite to the direction of the primary trend. This indicates a possible reversal in the direction of the primary trend.
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 AAPL 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: August 6, 2020
End date: April 29, 2024
a = 4.6684
b = 0.0003
s = 0.0879
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0003) – 1
= 12.07%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0879) – 1
= 42.15%
August 6, 2020 calculations
Top border of price channel:
Exp(Y321)
= Exp(a + b × X321 + 2 × s)
= Exp(a + b × 464 + 2 × s)
= Exp(4.6684 + 0.0003 × 464 + 2 × 0.0879)
= Exp(4.9891)
= $146.81
Bottom border of price channel:
Exp(Y321)
= Exp(a + b × X321 – 2 × s)
= Exp(a + b × 464 – 2 × s)
= Exp(4.6684 + 0.0003 × 464 – 2 × 0.0879)
= Exp(4.6374)
= $103.28
April 29, 2024 calculations
Top border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(4.6684 + 0.0003 × 1,826 + 2 × 0.0879)
= Exp(5.4145)
= $224.64
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(4.6684 + 0.0003 × 1,826 – 2 × 0.0879)
= Exp(5.0628)
= $158.03
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 12.07% per annum.
- AAPL price at the close of April 29, 2024 was $173.50 and was inside the primary price channel.
Secondary Trend
Start date: December 5, 2023
End date: April 29, 2024
a = 7.2392
b = -0.0012
s = 0.0224
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0012) – 1
= -34.59%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0224) – 1
= 9.38%
December 5, 2023 calculations
Top border of price channel:
Exp(Y1,159)
= Exp(a + b × X1,159 + 2 × s)
= Exp(a + b × 1,680 + 2 × s)
= Exp(7.2392 + -0.0012 × 1,680 + 2 × 0.0224)
= Exp(5.3302)
= $206.48
Bottom border of price channel:
Exp(Y1,159)
= Exp(a + b × X1,159 – 2 × s)
= Exp(a + b × 1,680 – 2 × s)
= Exp(7.2392 + -0.0012 × 1,680 – 2 × 0.0224)
= Exp(5.2406)
= $188.78
April 29, 2024 calculations
Top border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(7.2392 + -0.0012 × 1,826 + 2 × 0.0224)
= Exp(5.1604)
= $174.24
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(7.2392 + -0.0012 × 1,826 – 2 × 0.0224)
= Exp(5.0708)
= $159.30
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 34.59% per annum.
- AAPL price at the close of April 29, 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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