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 8.14% per annum.
- TSLA price at the close of May 3, 2024 was $181.19 and was inside the primary price channel.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 44.94% per annum.
- TSLA price at the close of May 3, 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 TSLA 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: May 3, 2024
a = 5.7337
b = -0.0002
s = 0.2196
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0002) – 1
= -8.14%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.2196) – 1
= 140.70%
December 3, 2020 calculations
Top border of price channel:
Exp(Y400)
= Exp(a + b × X400 + 2 × s)
= Exp(a + b × 577 + 2 × s)
= Exp(5.7337 + -0.0002 × 577 + 2 × 0.2196)
= Exp(6.0387)
= $419.37
Bottom border of price channel:
Exp(Y400)
= Exp(a + b × X400 – 2 × s)
= Exp(a + b × 577 – 2 × s)
= Exp(5.7337 + -0.0002 × 577 – 2 × 0.2196)
= Exp(5.1604)
= $174.23
May 3, 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(5.7337 + -0.0002 × 1,824 + 2 × 0.2196)
= Exp(5.7487)
= $313.80
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,824 – 2 × s)
= Exp(5.7337 + -0.0002 × 1,824 – 2 × 0.2196)
= Exp(4.8704)
= $130.37
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 8.14% per annum.
- TSLA price at the close of May 3, 2024 was $181.19 and was inside the primary price channel.
Secondary Trend
Start date: June 29, 2023
End date: May 3, 2024
a = 8.1243
b = -0.0016
s = 0.0852
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0016) – 1
= -44.94%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0852) – 1
= 40.60%
June 29, 2023 calculations
Top border of price channel:
Exp(Y1,045)
= Exp(a + b × X1,045 + 2 × s)
= Exp(a + b × 1,515 + 2 × s)
= Exp(8.1243 + -0.0016 × 1,515 + 2 × 0.0852)
= Exp(5.8180)
= $336.30
Bottom border of price channel:
Exp(Y1,045)
= Exp(a + b × X1,045 – 2 × s)
= Exp(a + b × 1,515 – 2 × s)
= Exp(8.1243 + -0.0016 × 1,515 – 2 × 0.0852)
= Exp(5.4772)
= $239.19
May 3, 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(8.1243 + -0.0016 × 1,824 + 2 × 0.0852)
= Exp(5.3129)
= $202.93
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,824 – 2 × s)
= Exp(8.1243 + -0.0016 × 1,824 – 2 × 0.0852)
= Exp(4.9721)
= $144.33
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 44.94% per annum.
- TSLA price at the close of May 3, 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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