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 43.77% per annum.
- BSX price at the close of May 4, 2023 was $51.94 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 93.87% per annum.
- BSX price at the close of May 4, 2023 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 BSX 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: June 9, 2022
End date: May 4, 2023
a = 2.1257
b = 0.0010
s = 0.0315
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0010) – 1
= 43.77%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0315) – 1
= 13.41%
June 9, 2022 calculations
Top border of price channel:
Exp(Y1,031)
= Exp(a + b × X1,031 + 2 × s)
= Exp(a + b × 1,494 + 2 × s)
= Exp(2.1257 + 0.0010 × 1,494 + 2 × 0.0315)
= Exp(3.6747)
= $39.44
Bottom border of price channel:
Exp(Y1,031)
= Exp(a + b × X1,031 – 2 × s)
= Exp(a + b × 1,494 – 2 × s)
= Exp(2.1257 + 0.0010 × 1,494 – 2 × 0.0315)
= Exp(3.5489)
= $34.77
May 4, 2023 calculations
Top border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 + 2 × s)
= Exp(a + b × 1,823 + 2 × s)
= Exp(2.1257 + 0.0010 × 1,823 + 2 × 0.0315)
= Exp(4.0020)
= $54.71
Bottom border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 – 2 × s)
= Exp(a + b × 1,823 – 2 × s)
= Exp(2.1257 + 0.0010 × 1,823 – 2 × 0.0315)
= Exp(3.8762)
= $48.24
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 43.77% per annum.
- BSX price at the close of May 4, 2023 was $51.94 and was inside the primary price channel.
Secondary Trend
Start date: February 16, 2023
End date: May 4, 2023
a = 0.6590
b = 0.0018
s = 0.0119
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0018) – 1
= 93.87%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0119) – 1
= 4.85%
February 16, 2023 calculations
Top border of price channel:
Exp(Y1,204)
= Exp(a + b × X1,204 + 2 × s)
= Exp(a + b × 1,746 + 2 × s)
= Exp(0.6590 + 0.0018 × 1,746 + 2 × 0.0119)
= Exp(3.8495)
= $46.97
Bottom border of price channel:
Exp(Y1,204)
= Exp(a + b × X1,204 – 2 × s)
= Exp(a + b × 1,746 – 2 × s)
= Exp(0.6590 + 0.0018 × 1,746 – 2 × 0.0119)
= Exp(3.8021)
= $44.79
May 4, 2023 calculations
Top border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 + 2 × s)
= Exp(a + b × 1,823 + 2 × s)
= Exp(0.6590 + 0.0018 × 1,823 + 2 × 0.0119)
= Exp(3.9891)
= $54.01
Bottom border of price channel:
Exp(Y1,257)
= Exp(a + b × X1,257 – 2 × s)
= Exp(a + b × 1,823 – 2 × s)
= Exp(0.6590 + 0.0018 × 1,823 – 2 × 0.0119)
= Exp(3.9417)
= $51.51
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 93.87% per annum.
- BSX price at the close of May 4, 2023 was inside the secondary price channel.
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